Set a conservative schedule for improvement (months, not weeks).

Automate the low-hanging fruit first (copying files, maybe, or centralized health-checking so you don't have to open logs).

For a lot of improvements you can make a business case other than your quality of life. Health-checking improves reliability, for example. But accept that these will be hard conversations that take a long time. Don't let others convince you this isn't a problem.

Research the tools that solve your problems -- it's easy to argue for adopting an industry-standard tool that solves an industry-standard problem.

Accept that certain pieces of the process will stay manual for a while.

Don't be afraid to go after small improvements -- if you can halve the difficulty, the remaining steps will fall away easily.