How did infantry on the Eastern Front evolve over the course of WWII?

I can't talk much abut red army or wermacht infantry but I know a bit abut Romanian Infantry, Romanian armed forces being the the largest force on the front after USSR and Germany.

Romanian infantry tactics and equipment are probably the ones that changed the most and quickest on the eastern front.

At the beginning of the war Romanian infantry units where armed with Rifles, LMGs(Light machineguns) and mortars but no SMG's (submachine guns). Even from the crossing of the Prut river Romanian units captured PPD's and PPSh's and troops used them on their own initiative. And after the disaster that was the Siege of Odessa the need for SMG's was recognised and the development of a romanian made SMG begun, as well as the purchase of foreign SMG's like the Beretta and the MP 40 as well as captured SMG's being put into service. By 1944 some romanian squads where mostly equipped with SMG's. Besides normal SMG's some StG-44 where also used by romanian troops.

Besides SMG's another quick addition to the arsenal was captured Russian AT rifles like the PTRS and the PTRD up to 40,000 of them. And by 1944 these begun to be Replaced with Panzerfausts and Panzershrecks and Raketen Panerbüchse 43

A strange addition during the war was the use of caputed Mosin Nagants as the standard sniper weapon. Probably do to them already having scopes and scope mounts.

Besides adding new types of small arms only thing the Romanian Armed Forces tried to upgrade during the war where machineguns. With the addition of MG 34's and MG 42's which where quite liked do to being lighter than the ZB-53 by heavy machine gun squads and the high capacity and fire rate by light machine gun squads.

A strange thing about Romanian armed forces is that they didn't bother with self loading rifles not even using captured Russian ones.

So as we can see from their small arms they have evolved from the interwar rifle units with MG back up to a mix of SMG's Rifles and LMG's. Mostly do to the need of CQC weapons and tactics do to city combat. While the lack of self loading rifles is probably do to the lack of need. As normal rifles are just as accurate and for fire rate MG's can be used, also do to logistics required to use SVT-40's on a large scale.

Though romanian armed forces get a bad reputation Romanian infantry had their own exploits and successes. One good example is how the Romanian Paratrooper Division managed to repel the Brandenburger assault on Bucharest, leading to the biggest defeat of the German special forces in WW2. Quite the achievement for a unit who hasn't seen combat before.

Hope this helped a bit.

Edit: some corrections and expanding on some ideas.

Edit 2: corrected the part about the Panzershreck.