B permit is also associated with tax at source, unless you earn more than 120k and maybe a couple other uncommon cases.
Assuming the choice of the B permit was already made, you have until March 2023 to figure it out. I suggest you ask the tax authority of your canton and the answer might depend on the exact country involved...
How can you have a B permit and not be tax resident? To maintain the permit you need to be in the country longer than you would need to be to become tax resident, no?
Wealth tax is calculated using world wide wealth to figure out the pro mille, but only charged on Swiss assets.
When you are on an L permit you are living and working in Switzerland. Which means you're tax resident and are liable for wealth tax already. However, on a L and B permit, if your income is below a certain amount and a few other conditions apply, you don't have to fill in a tax return and you pay tax at source - meaning that wealth tax is taken into consideration by the tax at source rate applied.
On a C permit, you're no longer on tax at source and WILL have to fill in a tax return.
Everyone should fill out a tax return at least once, so they have an idea if they are paying the right amount. No need to submit it, if you like the results.