we have over 300 projects in our mantis but me i am related only to about 10 projects normally.
wouldn't it be a good idea to have a page with a list of all projects and i can check my favorites, so only they are shown in select project list?
(plus group project "all")
the search field can still be present and mean to search all projects (not only favorites) as soon as i entered a letter.

new projects can be non-favorite as default.
it would mean internally to store a list of the favorites for each user.

for changing between projects, it would even be faster to just select the wanted project form the list compared to enter a fragment of the name and then select the wanted (or even scroll and pick).