I don't have a solution, just an explanation...
Some background information first. RStudio causes tons of disk IO (especially if your use git for version control, see the question you metioned) so any hiccoughs with disk access will result in noticeable lags in RStudio session.
H: is usually a network drive so it will be much slower than a local disk (C: is usually local) by its very nature and there is nothing we can do about it. Even the fastest HPC-grade fiber optic data center networks are slower than local disks. So whenever your RStudio project is on the H: drive you will see the lagging.
Now to your question:
I think the reason is that the regular scripts use the default RStudio working directory (where it stores active session data, environments for the suspended/persistent sessions, configuration settings, etc.) which i likely to be on C: under your user's home directory but projects actually create per-project working subdirectories. So all those working and temporary files will go to the network drive and any time RStudio reads/writes those files (which is very, very often) you would see the lags.
The solution is to never put your projects on the H: drive and use it for backups only...