The 13th century is this timeline's Age of (early) Industrialisation.
Steam engines, invented in the late 12th century, revolutionise manufacturing and mining. They create an insatiable thirst for coal, which sparks new territorial conflicts.
While production surges throughout the century in the Roman and Celtic Empires, in Norway, Sweden, Franconia, Burgundy, Venedia, Corvatia and along the Slavic Rivers, in Aksum, Sheba, Eran, on the Indian subcontinent and in South-East Asia, in Sui China, on the Swahili coast and the Liberian coast, and also in Celtic Wabanakiacum and on the Taino islands, transportation remains the main brake preventing an even quicker development. Heavy quantities of raw materials and produced goods cannot be carried across long distances; in many places, sailing remains the no. 1 means of industrial transportation. To this end, new waterways (canals) are built, using pound locks. Not only the quantity of products improves, but also their technical quality; wire being only one example, whose better quality allows for the development of various new technologies.
Nevertheless, early industrialisation in this timeline led to the construction of entirely new towns in the proximity of coal and ore deposits. Especially in the Roman, Celtic and Chinese Empires, these new towns were built in planned ways, primarily to prevent epidemics like those of the 11th century. Cheap, rational construction methods were used, so the towns all had the same boring look, but they provided their inhabitants with running water, sewers, cleaned streets and waste disposal systems, and often central heating, too.
Scientifically, the 13th century brought great progress in medical and pharmaceutical research, a renewed interest in natural philosophy (this time concerning physics, too, which had been neglected for centuries), as well as an increased politicisation of the rivalling schools of economic thought. Electricity remained a marginalised field of research and development.
In contrast to OTL, the early industrial age in this timeline coincides with a temporarily reduced interest in overseas explorations and colonisations. Transportation across long distances was a problem - and all its capacities being required in the industrial heartlands -, and new industrial technologies provided the field where adventurous explorers turned to.
But these two factors alone would not have explained the reduced European, Chinese and Indian interest in Atlantis, Caribia, the Taipingyang and Asambadha Anuttara (OTL: North and South America, the Pacific and Australia). They coincided with massive internal indigenous warfare from the Great Lakes of Atlantis in the North to the high mountain ridges of Caribia in the South. Although the wars between the Haudenosaunee and Sioux vs. the Mississippi city states, between Nahua-Mixtec isolationists and Mayan traders, as well as between Muisca Zipa and Chimor all had different backgrounds, courses of events and outcomes, there was always at least one strong party in these conflicts which opposed contacts with the foreigners from other continents. Hundreds of trading outposts were burned down, caravans massacred, the wells of colonies poisoned. Colonial engagement in Atlantis and Caribia was seen as a costly, unprofitable enterprise throughout much of the 13th century among Celts and Romans. The Taino-Ostrogoths concentrated on increasing trade among their various, quickly industrialising islands, and oriented themselves back West (towards Liberian Africa, Europe and the Mediterranean). Taino-Ostrogothic and Liberian syndicates dot the South-Western coast of Africa with trading outposts and small colonies, though.
The other major geopolitical event of the 13th century, which slowed down colonialisation, was the collapse of the Sui Empire. Stretching from the Arctic Ocean to the Mekong, from Mongolia to the Salish (on OTL Canada`s Southern Pacific coast) and across the archipelagos of the Lusong, the Maluku, the Papua, the East Coast of Asambadha Anuttara and the Gengjiuyunguo islands, the highly centralised Sui Empire was unable to contain secessionist uprisings, inspired by increasing education levels among local elites and growing anti-Sui nationalisms, fueled by the mismanagement of corrupt provincial magistrates, when several of these happened at the same time. At the beginning of the 13th century, Sui was still able to defeat a Mazdako-Tengrist rebellion of several Mongol federations led by Genghis Khan and conduct a genocidal punitive campaign, which drove many Mongols far into the Northern woods and shocked the educated classes back home in China and its vassal states. From the 1230s to the 1260s, though, secessionist movements occurred from Dai Viet and the Tai müangs over Lusong and the Maluku to Liuqiu and former Silla. Foreign powers like the Kalinga Alliance, Dvaravati, the Pyu cities, and Nihon, who had been wary of Sui hegemony and expansion for centuries anyway, supported many of these independence movements. Defeats on several fronts were followed by popular unrest in the Chinese heartland, and finally, the Sui dynasty was overthrown in the 1260s. A decade of revolutionary turmoil and esoteric sects followed, in which one in ten Chinese lost their lives, and during which Chinese outposts in Western Atlantis were temporarily abandoned. In 1281, one of the Taoist religious sects gained power over much of the Chinese heartland and established the Ming Dynasty, which legalised the secession of more than half of its territory through state contracts, and pursued a policy of ruthless Sinicisation as well as a persecution of Buddhists and other "foreign religions" in the remaining Empire. Many Buddhists flee to the newly established independent countries in the South and East. Meanwhile, in Northern Asia`s endless woodlands, the Kimek-Kyrgyz state becomes a Mazdako-Tengrist theocracy for almost five decades, in which the urban and indusrial development are halted and reversed and aggressive campaigns bring the Sinicised Turks of the former Uyghur Khaganate into their realm. When the theocracy collapses, the Mongol and Uygur groups secede, while in the North-West, a nationalist state emerges: Türkestan.
Another important development during the 13th century is the widespread use of pharmaceutical birth control by Liberian, Yoruban, Sao, Celtic, Roman, Swahili, Persian, Indian, Nusantaran and Chinese women. (Christian Sheba, Aksum and Armenia prohibited the pills.) Not only did they slow down population growth - which was another factor slowing down colonialisation. They also sowed the seeds of questioning patiarchy, open gender conflict, the emancipation of women and new family models, which unfolded with all their might only the following century.
In Northern Europe, Olavism becomes more moderate and Norway becomes a modern parliamentary democracy and nation state. The Swedish Kingdom finally turns into the Swedish Empire, controlling Finland, the Baltic region, Karelia and the lands of Vepsians, Galinds and Komi. Venedia becomes a Slavic nation state and moves its capital from Vineta to Wratislawa (OTL Wroclaw).
In Central Europe, Franconia`s coal and ore mines have fallen into the hands of Celtic corporations. Alemannia, which had enjoyed a leading role among the Germanic nations for a long time, falls behind economically.
In Eastern Europe, invasions of several Turkic federations are stopped and answered with a military conquest of vast lands by the Potamian Koinon of the Volga.
In Africa, the overstretched Gao Alliance falls apart, allowing Aksum and Luba to claim further rainforest territories. Unable to discover any treasures of the soils there, the interest shifts towards Luba-controlled Katanga and its wealth in copper. Luba`s relations with Celts and Romans become so strong that their Kiluba language begins to Latinise, and growing towns begin to bring forth a movement for democracy and against the absolute theocracy. On the East Coast, several Bantu nations establish stable and friendly economic exchange relations with Madagascar. Sui`s reduced trade volumes are quickly taken over by various Indian, Persian and Malay players, who continue to provide Africa with traditionally Chinese products like porcelain.