There will always be input lag, or more correctly in the case of PS Remote Play, network lag + input lag.
Remote Play is essentially a video feed from the console to the Remote Play app. How it performs depends on Remote Play settings, video bandwidth, video encoding / decoding, local network traffic, wireless interference etc. Ethernet is the fastest and most reliable network infrastructure, but there will still be lag in the video feed, probably in the vicinity of 100+ms.
The remote server "Stadia feature" of DualSense isn't as miraculous as it appears. All it does is remove one link in the chain by bypassing the computer (or console in PS5 Remote Play on PS4) to ping your local router directly from the controller. This will likely save only a few ms or so in each direction, which is almost no saving at all. All of the bigger lag inducers are still upstream on the local or wide area network.
Try the PS Remote Play app - it'll probably feel ok for single-player, but you should notice some lag for online multiplayer. It'll be better than not playing PS5 games at all, but installing the PS4 game version on PS5 will be less laggy than Remote Play. DualSense controllers don't (yet) work with XIM APEX, but I doubt Remote Play is significantly less laggy given the roundtrip saving is at the first and fastest link in the chain.
Let us know how you get on with the Remote Play test 
Ok now it's running with almost 0 input lag. I don't know if there is input lag, how to measure it?
At the moment it is nearly not noticble, I have to play some rounds in BOCW to test it.
My Setup:
PC --> Displayport
PS5 --> HDMI1
XIM Apex is in PC. Mouse, keyboard and DS4 V2 connected in XIM Apex.
Remote Play on PC. Start Remote Play. When it's started and running than change DP --> HDMI1, so you have the video source directly from PS5. (not the Remote with only 1080p and @#$% quality)
I have to play some rounds without it und with the setup, I will see, if I notice the input lag and get worser results.