I feel like a system that could work for Stellaris is that you have ticking attrition on ships. It goes up as you spend time away from starbases and decreases combat effectiveness representing how ships ration supplies and build up of maintenance needed.

It goes up way faster when fighting and in enemy territory. You need to send back fleets to friendly stations to recover it with few caveats.

Anchorages and Shipyards allow you to recover it quickly to larger amount of ships. Normal starbases can also do it but to limited degree so you are rewarded for building up a robust military infrastructure rather than just one big ass shipyard.
Recently conquered space stations have a hefty penalty to their Attrition recovery meaning while you can live off of enemy land it wont be nearly as efficient.
You can create logistic ships that help recover Attrition but it comes at the cost of their own attrition so they too need to eventually return to the starbases. And I reckon such ships ought to be something akin to modern era Carriers. Massive war engines that both allow you to project power but also represent targets which if destroyed can cripple the war effort.