Voice prompts vs. TTS voice settings (vs. system language?)

The language of the Audio Prompts can be set in Device Settings » Phone » Audio Prompts » Dialect

trux said:

...set in Device Settings » Phone » Audio Prompts » Dialect

This is just in case the watch is not connected to the phone. So you only have the watch and the earbuds. Otherwise, the language is set to Hungarian. Since the voice command is behaving so strangely, I haven't tested the latter yet, but I will tomorrow (I'll leave my phone at home).
But I would like it to be in Hungarian even if I have the phone with me and the voice command is actually coming from there and not from the watch.

I don't know what kind of watch you have, but my Forerunner 255 Music "sounds" completely different when it's done through the phone than when I leave the phone at home (and only have the earbuds and watch).
The setting you speak of - in my experience - applies to the latter case. For me, it worked super well so far (maybe more than a year) to have Hungarian set in the app, while the TTS voice language on the phone was also Hungarian. So even though the language of both my watch and my phone was English, the watch would speak in Hungarian in both cases.
My guess is that they have now changed it (I'll test tomorrow) so that it looks at the system language on the phone, rather than the TTS settings, which is not very good.
Anyway, if you don't believe me, try changing the dialect in the Connect app to say French (or any other language). Your watch, when connected to a phone, will definitely not speak in that language.

Adam Fulop said:

Anyway, if you don't believe me, try changing the dialect in the Connect app to say French (or any other language). Your watch, when connected to a phone, will definitely not speak in that language.

When I change the language on the phone, in the Device Settings » Phone » Audio Prompts » Dialect, the phone announces the alerts in the language I selected there, independent on the system language of the phone or of the watch. I would not advise it otherwise, of course. I have just retested it now, and it still works in the same way.

My watch (Instinct 2) does not support music / audio, and I cannot connect earphones to it, hence the prompts are always generated by the phone only.

trux said:

... in the Device Settings » Phone » Audio Prompts » Dialect, the phone announces the alerts ...

I apologise, but I was a bit careless. Well, the part I quoted back from you doesn't look like that in my case.
On the main screen, I click on my watch, then I select the watch from the paired devices (there is only this one), then under "Audio Prompts", at the bottom, I have the "Dialect" one. I can't get the phone to say anything. This is unfortunately a problem in itself, that you can't test the settings, but we'll leave that for now.
Tomorrow I will run by changing the language of the phone to Hungarian first. I will be curious. And after tomorrow, I'll change this "Dialect" to English (because it's now in Hungarian).

Adam Fulop said:

I can't get the phone to say anything. This is unfortunately a problem in itself, that you can't test the settings

All you need to do is starting a dummy activity and press the Lap button, to hear the announcement. Preferable select an activity where the lap button is enabled, although you can also initiate the lap (and the announcement) through the activity menu.

If the language in that setting is already in Hungarian, and the prompts are in a different language, try toggling it to something else, and then back to Hungarian again.

... err, actually even simpler: just tap the Volume option at the bottom - the phone then announces a test prompt in the selected language, without the need to start any activity on the watch.

Adam Fulop said:

I can't get the phone to say anything

If you do not hear anything, you may need to tune the volume up, in the ~5 seconds after having hit the Volume button

trux said:

... just tap the Volume option at the bottom ...

There is no "volume option" for me:

If you cannot scroll lower, and check whether the Volume is not hidden below the Dialect option (it is there for me, with Instinct 2), then do as I originally wrote - start any activity with the lap button enabled, hit the Lap button on the watch, and immediately tune up the volume on the phone, in order to hear the prompt, in case the volume for the announcements is set to zero, which may sometimes happen.