I did some more testing with this [new to me] functionality, and I need to correct myself in some respects. All tests done 2/2022 on Windows 11 with Lazarus 2.2.0/FPC 3.2.2.
I could finally debug my daemon regardless of whether I ran it as system or under a specific service user account, and it is not necessary to use the same account for Lazarus and the daemon. All I needed is to run Lazarus with elevated privilege. The handling of the debugger controls in Lazarus needs a bit of attention and practice when one does it the first time. And FPDebug didn't work, "Run - Attach to program" never got active, unless I changed the debugger in project options to GDB.
PSExec has many options which may be handy in some scenarios, but is not specifically necessary, with one exception: Windows does AFAIK not allow one to "runas" Lazarus under the "system" account, so if anyone, for any reason, wants to run Lazarus under the system account, he needs to do that using PsExec. For my purposes "run as administrator" from the Lazarus.exe context menu did the job nicely.
IsDebuggerPresent is a great aid for Windows, I still wonder whether there is an equivalent for Linux. Sure, there is that "change loop variable using the debugger" workaround mentioned above, but ... :-)
Thanks again to Martin, whose initial post showed me the right way!
Armin.