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You have to test more.

I can provide some more info though. So languages do affect the procedure. I personally set up all the commands I use in IFTTT directly - so I can use german trigger words for example - and I can tell you, that using "english" for Google Assistant in IFTTT with an english trigger word, didn't work for me in practice (Google Home set up as "german"). I had to set up my triggerphrases in german.

So different "written text" recognition and handover imho is expected, if f.e. your Google Home is set up in a different language than english.

Upercase/lowercase probably wont make a difference (if I do a google voice search for Kodi Pause on my Android phone, (without assistant activated), it comes back as KODi pause, so - yeah... ).

If you dont use the "single IFTTT action" method (Kodi $) which transports everything you say to the Glitch server and that then disects it further, you are only producing the phrases that - if detected by google, will tell IFTTT to push the commands you could also input on the test site to the server.
(That is if you are not using $ (for a number f.e.), in which case that number would have to be detected, and handed over as a variable.)

So on that base level - getting different results on the test page and on IFTTT doing something is impossible. Set up your own keyphrases in IFTTT and test with them - for the navhome, navback - etc actions. Just make sure that they trigger the corresponding URL and see what the results are.

If you use the "single IFTTT action" method (Kodi $), everything that gets spoken after Kodi will be handed to the glitch server as a variable - and the glitch server then does RegEX (Regular Expressions) parsing on the text. This is VERY 'down by the book' as in text has absolutely be written correctly, minor inconsistancies can throw it off, text incoming has to be exactly as expected, and so on and so forth...
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In principle. All Webhook does, is first - get triggered by a trigger (f.e. Google Assistant), and then send over a request to the Glitch webserver - the same way the test page would do. It literally calls the same 'modules' (entry points). So if phrase is recognized correctly - there should be no more points of failure from that point forward (if you dont go the single IFTTT action route).

Webhook really only is "if phrase is detected" "visit website" and in some limited cases "hand over variable (think number)".

Also I never get 'error messages' on Kodi itself. So thats also something interesting to look into. (I've integrated the navback command at least, and it works as expected. I used triggerword 'back' which I have to pronounce in my best Arnold Schwarzenegger impression (german pronounciation) for it to trigger the command. (Home and IFTTT action set up in german).

so are you saying you setup a IFTTT applet for every command you want to send?  Do you have a snapshot of how that would look?