Perhaps could break down departments and give them a scale to allocate resources to?
Performance Analysis 1, 2, 3, 4, 5
Physiotherapy 1, 2, 3, 4, 5
Sport Science 1, 2, 3, 4, 5
Recruitment Analysis 1, 2, 3, 4, 5
Perhaps if you've allocated enough money to move up a level (or perhaps like scouting budget) it allows you to hire more staff rather than request it, likewise you need to hedge back a bit and move down a level you need to let go off a staff member.
Performance Analysis perhaps upgrading to x level allows you to unlock/hire an opposition analyst, data analyst etc and therefore you get provided more information pre-match only when you have those staff members in place?
Physiotherapy, as you up the levels perhaps you have access to a pool for recovery sessions, an extra sports therapist.
Sports Science, perhaps you have a nutritionist (even if not a hireable staff member as it could be tricky to do it, but provides a boost to things like fitness levels, nutrition is now huge in academies as well)
Recruitment Analysis - Perhaps access to a data scientist as you get higher levels.
The other thing would be as you allocate more resources for higher levels, your wage budget for the roles in those departments then increases. This could allow more specialisation in backroom staff that you want to prioritise, you could have world class analysis facilities but lower league sport science support because you as a manager don't believe in sport science for example.
This method/something like the scouting budget would allow for a fluid adaption of what you want from a backroom staff. For big level requests like building/upgrading a new analysis/physio room, sports science area etc could then be like it is now, but you can break down which departments you want to upgrade.