Do spouses of UK citizens who hold a non-EU passport have to apply for a Schengen VIsa now

The short-stay visa requirement in the Schengen area was always based on citizenship. If your spouse comes from the 60+ countries listed in the so-called “annex II” (covering most of the Americas, non-EU Europe, UAE, Japan, South-Korea, Malaysia…), they can visit visa-free. Otherwise, they need a visa. That was the case before Brexit and will continue to be the case. The same rule applies to third-country nationals who do not belong to the family of an EU citizen.

What changed are the rules around getting that visa. For people covered by the EU freedom of movement (including the family of British citizens before Brexit), that visa must be free of charge and valid reasons to refuse a visa are very limited. For other people (including most British citizens' spouses after Brexit), you have to pay a visa fee and submit a lot more documentation (e.g. on your financial situation).

There is an additional exemption for spouses of EU citizens residing in another EU country with a residence card as a “member of the family of an EU citizen” (article 10 or 20 card, it should explicitely say so on the card). In that case, it's not necessary to apply for a visa for a short visit, even if you come from a country whose citizens usually need one. The exemption should still apply to British citizens who settled in the EU before January 2021 and their family but otherwise ceased to be relevant after Brexit.