Continue project? Or....

Dewit.

DON'T DO IT!!!!

It depends on your project (or more specifically how much you have left for it to be completed), upgrading Aversa costs around a week and a half of time or less (that's about how long it takes me to get 20k feathers). If you are only in need of feathers to finish in then keep going, otherwise give Aversa a try.

Tbh the only way to stop the Horse teams right now is anti-cav units and Raven TA users. Building up a M!Robin (hoping to eventually transition to a +10 Lyon TA build since he has better bulk but as I'm about to point out below) of all units cause I just can't deal with B!Lyn + B!Veronica anymore. Offensives nukes that I can't even counter attack against, so i need someone who can just shrug off all their attacks (which a +10 +atk LnD3 Firesweeper Bow B!Lyn is gonna laugh at me for even attempting)

As long as Aversa can reach the HP threshold to debuff everyone, she's fine where she's at. Great unit but with her STILL not in the Grail shop, you're better off getting someone else that doesn't require the material you need to farm to even get her. Just try to maximize her HP, get her to 5*, and debuff everyone you can. Panic Ploy might even be an interesting choice to run on her if you meet those requirements too (and with Valter in the shop that might be a good investment).

Right now my Aversa is just a Base set with HP/Res 2 seal and plugged in a few easy to get skills and abilities to round her out. Her base kit is fairly decent surprisingly. A nice low investment F2P unit.

Tl;dr. YES, but have someone else around to actually deal with horses more roughly like a Wolf Tome user or a Raven Tome TA user. She's a nice low investment to have around to help.

Honestly depends. You don't have to have a complete anti Cavalry unit to stop horse teams. If Reinhardt is giving you trouble, or any other magic cavalier (like Veronica), then I'd recommend investing in a mage tank. If Brave Lyn, is the one giving you trouble, or any other physical-attacking cavalier, then invest in a physical tank. Even though Distant Counter units can't counter Lyn, having someone on your team that can tank her can still help tremendously.

Quick note, if you invest in a magic tank, don't I wouldn't recommend investing in a Lance unit unless you have multiple mage tanks on your team. Reinhardt's tend to carry Lancebreaker, and I don't think there's any unit aside from Jagen that can tank a Quad-hardt.