I ran into:
...
(gdb) catch exception some_kind_of_error^M
Your Ada runtime appears to be missing some debugging information.^M
Cannot insert Ada exception catchpoint in this configuration.^M
(gdb) UNSUPPORTED: gdb.ada/catch_ex_std.exp: catch exception some_kind_of_error
...
and indeed, after installing the debug info package libada7-debuginfo, I got instead:
...
PASS: gdb.ada/catch_ex_std.exp: compilation foo.adb
PASS: gdb.ada/catch_ex_std.exp: catch exception some_kind_of_error
PASS: gdb.ada/catch_ex_std.exp: caught the exception
PASS: gdb.ada/catch_ex_std.exp: print $_ada_exception = some_package.some_kind_of_error'Address
...

Then I wondered if it would be possible to use gnat_runtime_has_debug_info in this test-case, say using a require.  So I tried:
...
 require allow_ada_tests
 
+require gnat_runtime_has_debug_info
+
 standard_ada_testfile foo
...
and removed the debug info package, but I ran into the same UNSUPPORTED as before, in other words, gnat_runtime_has_debug_info returned 1.

The reason is that gnat_runtime_has_debug_info tests for presence of a symbol __gnat_debug_raise_exception, and while the debug info package is not installed, the shared lib is not stripped and we find it here:
...
$ nm -D /usr/lib64/libgnat-7.so | grep __gnat_debug_raise_exception
000000000025ac7c T __gnat_debug_raise_exception
...

Interestingly, when looking at the "Your Ada runtime appears" error, it triggers for the very same symbol, and it triggers because msym.minsym->type () != mst_solib_trampoline, instead it has:
...
(gdb) p msym.minsym->type ()
$4 = mst_text
...

Concluding, there seem to be two levels of debug info support, minimal and full, and the minimal one seems to be sufficient to allow gdb.ada/ptype_tagged_param to pass, while the full one is required for gdb.ada/catch_ex_std.exp.

It would be good if we had gnat_runtime_has_debug_info variants to distinguish between these cases.