Not that much. Ownership is more of a money eating machine than a time consumer for the owner who has someone do their maintenance.
Your AI/A&P takes care of your tech logs. You just fly it, schedule maintenance with them, deal with your insurance. Your LI may or may not have a flying exclusion. Examine the contract. If nothing is there, you're good to go. If it is, you may have to pay extra.
I do my own maintenance and annuals on my homebuilt so there's that work once a year and from time to time for unscheduled fixing and tinkering, but otherwise, not much direct activity.
A typical owner just flies and pays bills. Lots and lots of bills. If the financial burden is light relatively speaking, that is, it's money you could use to light a cigar without giving you a heart attack, you can enjoy it.
If the costs are a burden and make you sacrifice other things that you'd rather not, it takes out most of the enjoyment. The old saying goes, like with large boats that are bit more than someone can afford: the best days are the day you bought it, and the day you sold it.