is this a bad idea? plan on mixing some topsoil in, but dont have very much on hand
Not just alkaline, but extremely high salt concentrations. There might be some ocean plants or Dead Sea flora that could tolerate wood ash, but my guess is it will essentially act as a herbicide
You’re better off digging up some dirt from an abandoned lot
Tomatoes are heavy feeders and you’ll have to fertilize to get a decent yield. If you don’t want to buy stuff, nitrogen is easy you can just piss in your watering can (5-10x dilution, keep it off the leaves). For phosphorus and potassium you can use your wood ash although there’s better sources out there. Compost would be best if you can get it.
Don't plant anything in straight wood ash.
If you don't have potting soil, mix some compost with topsoil. If you really want it to be alkaline, add like 5% ash. For stuff that needs good drainage, add some sand and/or fine gravel to the mix.
Regular outdoor potting mix + coffee grounds or fish meal beneath the plant. You want the soil to be slightly acidic, not basic.