The next presidential election is in 2024; the next parliamentary one is in 2025. Sandu has a single-party majority government and has always had substantial opposition, so I’m not sure the protests indicate a lasting sea change in public opinion.
In terms of damage to (relative) European unity, the storm clouds are worse in Bulgaria, Italy and Slovakia.
If Russia faces the eventual risk of ammunition shortages, perhaps they will seek to draw stocks from occupied Transnistria. Moldova has long desired the dismantling of the Cobasna ammunition depot and other sites, which have repeatedly been cited by Russia as reason to maintain their deployment on Transnistria. The trouble with this strategy is that Ukraine could attack the depot if they feared it was to be used against them.