Manually edited label not applied from a preset (when applied by user)

Is your feature request related to a problem? Please describe.
When the global option automatically update module name is set to false, saving a preset with a manually edited label, then applying such preset to a new image (or new module instance), does not set the manually edited label. My understanding/expectation is that a manually edited label should be saved and applied (regardless of the option automatically update module name).

Note that it does work like I expect, i.e. the manually edited name is correctly set, when the preset is auto-applied (I used that on all my images); it does not work only if the preset is applied manually.

Step to reproduce

1. Open a module (let's say denoise (profiled)), change some settings (mode = non-local means)
2. Edit the label ("NLM")
3. Save a preset ("Mode: Non local means")
4. Add another instance of denoise (profiled) (labeled by default "1"), apply the preset "Mode: Non local means" (or directly create a new instance from the preset menu).
5. Label stay "1", while I would expected it to be set to "NLM".

If in 3. you define an auto-preset (let's say for all image) and then:
4. reset the history, so the preset is automatically applied
5. The label of the module is correctly define to "NLM".

Describe the solution you'd like
Always applied a hand-edited label from a preset (make the user-applied preset behavior consistant with the auto-applied preset behavior).

Alternatives
Switching to automatically update module name = true (were the manual name is correctly applied), but it has other effect (the main one) that I'd rather avoid.

Additional context
Not sure if my request is just a missing part of the initial implementation (see PR https://github.com/darktable-org/darktable/pull/13998) or if it's voluntary, maybe @TurboGit you recall what was your intention.

Reproduce the issue using the listed denoise (profiled) preset steps, comparing manual application with auto-application. Review PR #13998 and trace the preset application path to determine where the manually edited label differs; done means a manually applied preset preserves the edited label while the automatic behavior remains consistent.