By default, the vscode-zig extension provides formatting by itself and does not rely on ZLS unless the zig.formattingProvider config option is set to zls. There have been other recent reports about the vscode-zig formatting not working properly but me and @SuperAuguste have not been able to reliably reproduce or identify the cause of this issue.

One possible reason could be the fact that zig fmt has recently become just in time compiled when it is first used. This means that formatting for the first time will take some time until the formatter has been compiled. This can be easily noticed when running zig fmt --help with a new Zig version or cleared cache.

Until this has been resolved, you can switch to ZLS as the formatting provider which does not have this issue as far as I can tell.

Lately, I've been getting this freeze almost every minute or so. I gave "zig.formattingProvider": "zls" a try, and it seems it's working! My saviour! Thank you! The question is then what kind of formatter I was using? The option was set to extension. Also, does it mean the "zig.zls.*" options are irrelevant unless switched to the zls provider?

Both formatting providers behave identical. extension means that the vscode-zig extension runs zig fmt behind the scenes. zls means that the vscode-zig extension will ask ZLS to format the file and ZLS will run the standard library code that implements zig fmt (ZLS basically contains the zig fmt command). The zig.formattingProvider is only about formatting the zig.zls.* are about all the other ZLS features that are not formatting.

The zig.formattingProvider is only about formatting [and] the zig.zls.* are about all the other ZLS features that are not formatting.

Sorry, I didn't really understand the answer. Isn't, say, zig.zls.enableAutofix part of the formatting? If not, then what is it part of?

Also, I tried to disable the formatting altogether but realized that I can't (through options) unless I disable the extension itself. Here are my options (relevant parts):

  "zig.formattingProvider": "off",
  "zig.zls.enableBuildOnSave": false,
  "editor.formatOnSave": false,

Interesting to note that when it comes to formatting other files (eg. json), the formatOnSave set to false effectively disables the feature. So it seems the extension does not respect the global option and formatting is executed no matter what.

Update: "zig.formattingProvider": "off" indeed disables formatting (I just needed to reload the editor). However, solely using "editor.formatOnSave": false doesn't disable it.

Sorry, I didn't really understand the answer. Isn't, say, zig.zls.enableAutofix part of the formatting? If not, then what is it part of?

Autofix may appear as a feature build on top of formatting but they are actually independent. You can use autofix without formatting and the other way round.
When talking about formatting, I refer to all changes that zig fmt does. All other text edits you see are autofix from ZLS and don't rely on zig fmt or the zig executable in general.

The zig.formattingProvider only concerns itself with formatting and not autofix.

However, solely using "editor.formatOnSave": false doesn't disable it.

The vscode-zig extension overrides the editor.formatOnSave option for Zig which takes priority over the "ordinary" editor.formatOnSave option.
To disable formatting on Zig files in VS Code, the following needs to be added to settings.json:

"[zig]": {
  "editor.formatOnSave": false
}

This should have hopefully been fixed by ziglang/vscode-zig#222 which is in the vscode-zig 0.5.9 release.
If this still happens, feel free to report this to vscode-zig.