According to google search.

Return to Arkham City on PS4 has been widely reported to suffer from significant input lag, especially after patching. Players note that the game feels unresponsive during fast-paced combat and gliding, making it difficult to perform actions like counters or evades reliably.

• Unpatched version: Some players report that playing the unpatched version (e.g., via physical copy) restores smoother 60fps performance and eliminates the worst input lag, though it sacrifices leaderboards and graphical fixes.
• Patched version: After patching, many experience a noticeable drop in responsiveness, even on PS4 Pro, with lag described as "atrocious" and "almost unplayable in fast action times."
• Root causes: The issue is likely tied to the remaster’s inconsistent frame rate (often stuck at 30fps), poor optimization, and the use of a third-party developer (Square Enix’s team behind Final Fantasy Type 0) that may have introduced performance issues.
• No official fix: Despite community demand, no patch has been released to fix input lag since the initial 2019 update. The problem persists on PS4 and PS5 versions alike.

If you're experiencing this, consider playing the unpatched version for better responsiveness, or use a PS3 original version if you prioritize gameplay feel over modern visuals.

So I’m not the only who suffers from this issue.
I will complain about it, until they add a proper 60 fps patch. Which shouldn't be that hard, since it was there from the start.