To provide some additional information.
I've been using power strips for years. Most of the outlets in my home are the 3 prong type, but are not grounded. My room has a 2 prong ungrounded outlet. I added a 2 to 3 prong adapter and added a power strip. No issues.
In the living room, where my tv is, the outlet is a 3 prong ungrounded outlet. I plan to upgrade my power strip from a 12 to a 22 or 24 outlet power strip. I'd plug in gaming consoles along with upscalers.
What I don't want to have happen is to plug in a 22 outlet power strip and have a wiring fault occur so that the power strip doesn't function. Although it doesn't seem like a problem would occur.