The Russian Chess Federation's move from Europe (ECU) to Asia (ACF) takes effect on 1st May. In the meantime players with RUS membership may not play FIDE rated chess. Those Russian players who have transferred to FID as Russians are eligible to play in European championship competitions until that date.
So, the European Individual Chess Championship, which start today, March 3, in Vrnjacka Banja, Serbia already has 48 players registered under the FIDE flag.
However, FIDE has introduced new rules for players wishing to change federation to country member federations (i.e. not FID). According to this chess.com article:
Normally speaking, a federation accepting a new player has to pay a 5,000-euro transfer fee to FIDE. However, much more significant is the "compensation fee" that the Russian federation would receive if a player leaves. For players rated 2700 and above, that is as high as 50,000 euros; for players rated 2600 to 2699, it's 30,000 euros.
The FIDE Council decided that all transfer and compensation fees due to the CFR are waived for players registered there. They have until August 31, 2023, to decide on a transfer to one of the ECU's member federations and will have the right to represent the new federation in all official individual events of FIDE from the next day of submitting their application without any restrictions, provided that all other conditions for the transfer have been met besides paying the fees.
The article goes on to claim that players are better off playing in European competitions than Asian:
After the CFR leaves the ECU, these players will lose some of the benefits they have in Europe, such as participating in the different European championships. According to ECU President Zurab Azmaiparashvili, the ACF is "several years behind" the ECU in terms of structure and opportunities for players: "As part of the ECU, it will be an easier life, also for trainers," he told Chess.com.
The first Russian player to take advantage of this (that I have seen) is Alexandra Kosteniuk who announced in a tweet today:
Now it’s official. Representing Switzerland since 03-03-2023
So, I suspect that in the long run the answer to your question is that it will make little or no difference for the simple reason that FIDE have made it possible for Russian players to move cost-free and without delays to the European federation of their choice and most are likely to do so.