First, websearch "octopus outlet fire". Then...
Manufacturers and safety agencies really don't want to approve anything that might encourage people to overload circuits and start a fire. And if you have power strips plugged into power strips it's too easy to make that mistake. Even extension cords are frowned upon because you might eventually forget and plug another power strip or other high load into the extension cord, or plug the power strip into an extension cord with lower amperage rating, or plug the extension cord feeding the power strip into another power strip
Really, UL doesn't much like power strips or extension cords at all though they recognize the necessity.
But realistically, people do it, and it works, and it's ok if you can take the precautions that UL doesn't trust you to take and ensure that the next person who touches it does likewise.
If the power strip is lightly loaded (worst case with everything turned on is well below its rating), and the new load is small (as the LED lights probably are) and doesn't push that worst case over the rating, AND you make sure the extension cord can handle that worst-case load, AND you make sure everything is very visibly labelled so nobody can forget and overload it later... Well, it's still not a good practice, but you are at least being unsafe in the safest way possible.
And you should replace it with a proper long-corded power strip, and/or have another outlet put in where you now need it, at your earliest convenience. Because no matter what signage you put on it, someone is eventually going to try to plug in at least one more device, and overloaded extensions and outlets are notorious for starting fires.
"WARNING:* Do make absolutely sure the extension cord is rated for the load you will be putting on it; ideally, the same rating as the power strip. And it would be a good idea to test this before hiding it -- plug everything in, turn everything on, and make sure neither the extension or the power strip becomes warm to the touch either immediately or after some time of usage. If either warms up, at any time, UNPLUG IMMEDIATELY. Ditto if you smell anything that suggests either is cooking itself. And, I say again, do switch to a proper solution at your soonest opportunity.