The crankset only cares about front derailleur:
- A "trekking" style crankset (26/36/48) may not work with chainline of "road" front derailleurs, so chainline can be an issue
- The curvature of the largest chainring should match the curvature of front derailleur cage
- A triple crankset uses a different style of front derailleur from that used with a double crankset
If you maintain the chainline, big ring size and number of chainrings, you'll have no issues.
A chain can be a limiting factor only if the chainrings are intended for a grossly different chain width. For example if you have a 10-speed crankset go ahead and use it with 9, 10 and 11 speed chains. However more than one generation mismatch could be an issue: for example if you have an 11-speed crankset I don't think you can successfully use it with an 8-speed chain.
The move to Hollowtech II from Octalink that you suggested is a wise idea. Octalink was a major failure, its left crank arm loosened and the bearings had so little space the bottom bracket fails early. Hollowtech II fixes the problems of Octalink.
The 2x11 vs 9-speed chain could maybe be an issue. I would see if there are any 10-speed cranksets for Hollowtech II available. However, if you run into issues there are plenty of third-party manufacturers that make 9 and 10 speed chainrings but the odd chainring bolt pattern used by FC-R7000 will be an issue.
I wouldn't buy any crankset that uses non-evenly spaced chainrings bolts. So I wouldn't buy FC-R7000 because it has a "proprietary" bolt pattern used only by Shimano. Try to see if you can find any crankset with 5-bolt 110mm pattern. Finding new chainrings for the crankset 20 years from now when the non-evenly spaced bolts won't be in fashion anymore will be a major headache. However, for 110mm 5-bolt cranksets, you could find chainrings 20 years ago, you can still find chainrings today, and in 20 years chainring availability won't be an issue.
Note that "MTB" and "road" style bottom brackets and cranksets are not cross compatible in Hollowtech II. If you have a "road" crank, you must use a "road" bottom bracket.