Is FieldByName a function or a property?
1) properties with getter
property Foo: TSomeThing read GetBySomeMethod;
For those the compiler does not generate debug info. So they can not be inspected. There is a bug report to add that to the compiler. But currently I have no feedback from the compiler team when that may happen (once it has happen, it then also needs to be added to the debugger).
It may (sometimes) be possible to call the function "GetBySomeMethod" from the debugger / see below.
2) Function
For most (but again, not all) functions the compiler will add info on how to call them.
It then depends on what your debugger setup is. You may be able to call them and see the return value. (but calling them will execute them, and may have side effect / change the state of your app / but that happens in other IDE/languages too, afaik incl. Delphi)
Tools > Options > Debugger > Backend
https://wiki.freepascal.org/Debugger_Setup#Setting_up_the_debugger_backend_for_the_IDEThis will tell you which "Debugger backend" you use. If you are on Windows or Linux, and have an i386 or x86-64 CPU then it should be set to "FpDebug".
Then, and only then, you can call (some/most) functions.
If you are on Mac, or have arm/aarch then unfortunately you can not.
To enable function calling from the debuggerTools > Options > Debugger > General: CHECK "Allow function calls in watches"
(if you are on Lazarus 4.n then ignore the "BETA" in the name)
Then add a watch
FunctionName()
The "()" is important !!! (and if the function needs args, then specify them)
In the watch property check "Allow function calls"
In your case that would be
qry1.FieldByName('F1')
Which (hopefully / if it works) returns the object, and you can then inspect this.
If you want AsString, and if that is yet another function then it would be
qry1.FieldByName('F1').AsString()
// not sure if multiple calls will work
If it is a property then it may be
qry1.FieldByName('F1').GetAsString()
As to if the debugger will actually find the function (if the compiler adds the info about it), that may depend on if you are on Windows, or Linux.
IIRC (but its been a while) on Linux you must have debug info for the unit in which the class with that method is declared.
And IIRC in either case, the function must be used in the app or the compiler may optimize it away.
I haven't tested any of that, I don't currently have any DB app ready to test.