Prevent Safari from opening minimized window

One way is to use built-in way to open new window while clicking on link. ⌘ + , to open Safari preferences > Tabs and one can see following options:

So ⌘ + ⌥ + click will open link in new window and makes it active. By adding ⇧ will not make new window active.

Also - what action you call minimizing? Because I can't reproduce any sudden window opening if window is minimized (⌘ + M)

Might not be the answer you're looking for, but on Safari 15 and up, a possible solution is the Tab Groups feature to separate out tabs into different groups.

From the Apple Support page for Tab Groups:

You can organize tabs into groups that make it easy to quickly switch between groups of related websites.

Tab Groups can be accessed from the sidebar (View > Show Sidebar) and you can create them with the plus button located in the upper right there. Then you can move existing tabs into the appropriate Tab Group.

Using Tab Groups, you can separate tabs for your different projects into different Tab Groups. When you open other links, they'll open in your local Safari tabs and not in the Tab Groups for your projects. If you want to continue work on the project you can use the sidebar to open a Tab Group again.

There's no simple way to do exactly what you're asking, but you could install Safari Technology Preview (or another browser of your choice) and use it for your project (with your minimized windows), while leaving "regular" Safari to handle links. Alternatively, change your default browser in Preferences -> General so that Safari won't handle http[s]:// links by default.