>Russia deploying another 200,000 troops
It is a very hard task even to just deploy, let alone with any gain. In February after months and months of training Russia has deployed to Ukraine about that number of the best forces it had (like Kantemirovskaya tank division). We've seen how it went.
The newly mobilized forces, even after 2-3 months of announced training, will be an order of magnitude worse with worse hardware (that if China doesn't help - there is a reason Putin made the announcement right after the Shanghai Organization summit, may be China promised something, though that would most probably accelerate US hardware to Ukraine). Deploying such forces to a battlefield, especially a one like in Ukraine - as they say it is much more harsh than even Chechen war - one risks loosing them as they come. For now Russia announced plans to use them initially in the 2nd/3rd lines of defense.
As an example - during recent Harkiv counter-offensive by Ukraine Russia was trying to stop Ukraine by throwing in significant new, recently recruited, additional forces without any staging, battle order forming, etc. - those forces were just destroyed as they came by Ukraine as a result.
Giving Ukraine more and better weapons will nullify any Russian number advantage and thus is the shortest path to end this war.