Nested vaults eh? I tried that the very first time I downloaded Obsidian. I’ll admit it sounds like a good idea to have the best of both worlds. But one must be aware that there could be serious bugs doing that. The devs don’t recommend doing it even though the app allows it. Here’s one example of someone losing data doing that, especially with daily notes. I know it could be rare, but something like that happening once is one too many times since you never know what you could lose at what time.
Here’s what I’d suggest until this becomes officially supported after there’s been enough testing of nesting vaults. Move the project folder out of the vault entirely and open as a separate vault and work on it. Once done, recreate the folder in the main vault, and move back only the files from the project vault. One could also just remove the hidden .obsidian folder from the project and move the folder back but moving the notes should be easier for most people.