There are a multitude of factors that influence tank design in a country. Some of those can change with a relatively recent POD, others are owned to long term impacts or unchangeable factors like geographic realities.
Take the German example. Otl WW2 it was cut of from critical ressources, had a numerical disadvantage it could not change (at times they were outproducing their ability to man new vehicles!), their main theatre had relatively open plains, the industry was better at producing quality than quantity. Operational needs and doctrine requirements changed over time. Until the Panther and Tiger I available infrastructure was also a major concern.
That led to the otl design decisions: pre war (and again post war) priority on mobility and crew layout over firepower and protection. Later in the war on the defense crew survivability and long range firepower became higher priorities. Always a desire to have tanks that are able to balance the unavoidable greater enemy numbers. They made mistakes obviously, especially in going for ever heavier tanks, but the fundamental makes sense: a German T-34/M4 spam attempt would have gone even worse given the circumstances.
Now what of that can change?
Manpower depends entirely on the enemy in atl and the timing of a conflict. In a contained war with just say Poland or France, not an issue, especially with a longer build up that allows training peace time reserves. Anything approaching otl ww2 still leaves Germany scrambling for Manpower.
Resources again depend on the type of conflict. Otl at various places they had to use steel in place of aluminium or a suboptimal kind of steel, despite the obvious and known disadvantages. With free access to the world market that may not be necessary to the same extent.
The industrial structures were developed since the 1870s, so with a late POD are difficult to change. Otl the Germans tried to change from their craftsmanship base to a more mass production approach during the war, but it had all kinds of problems (e.g. a massive drop in quality control) and they mostly went back postwar. Now changing the industry is not impossible, but the later the POD the harder it is.
The requirements discovered during a war again depend on the war. Lessons from a war entirely fought in Western Europe will radically differ from a Russian campaign.
That is wartime though. Doctrine wise prewar influences will largely stay the same: German focus with a POD after 1815 will be on a fast war of movement and flexibility of command. Mobile tanks with decent crew comfort for the former, three men turret, good optics and as many radios as possible for the latter. With a POD post Versailles a tendency to push technical limits and tunnelvision in specialisation is also likely: if you can't go into serial production anyway, it makes sense to try for the best design for a specific job possible.
Overall I'd say pre-war doctrine is the main driver for pre-war/early war designs, the industrial side will (beyond the basic budget available) always be secondary: if the French anticipate a repeat of trench warfare and focus on pre-planning down to tactical level, the need for heavy armour will still be dominant, while low-mobility or a single-man turret are not significant drawbacks. If the British still draw a very sharp distinction between Cavalry and infantry tanks, the differences between the two types will persist etc.
