Hello, and greetings from Germany.
I'm sorry, but my first post here will be a rather negative one...
I don't like Tilly, and I don't see that I ever will. Here's why:
1.: Tilly is a comic relief character... and bad one at that
Tilly follows the "stupid and/or incompetent and/or clumsy and/or annoying = funny" formula, and frankly, I hate characters like that. Especially when they are designed to "fail upwards", meaning that they can say or do stuff that just makes you want to scream at the screen "NO, you stupid fuck!", and, through sheer luck or several inches of plot armor, still come out on top. I call it "the Jar Jar Binks Syndrome". Let me explain:
When we first meet him, Jar Jar has been exiled by his own people because of his clumsiness and stupidity! Yet he "wins" the battle against the robot army on Naboo and becomes a war hero, even though he should have been the first one to go down with the first shot fired. The only reason he survived is, that in the mind of George Lucas he was "the Chewbacca for a new generation! Oh, the fans will love Jar Jar!" Later Jar Jar even becomes a Representative in the Galactic Senate. How? What does he know about being a diplomat? What knowledge does he possess in this highly complex (and sometimes dangerous) field of work?
Sure, we have seen Tilly showing some mad negotiating skills, but "skilled" does not equal "competent". Jar Jar was skilled at foraging in the wilderness. He could have survived on his own. But overall he was a stupid and incompetent character that was protected by the plot. Like Tilly.
A competent Tilly would not have forced themselves into Hannelores private life the way they did. A competent Tilly would have done their homework better, by maybe doing more than just reading a dossier. A competent Tilly would have shown basic empathy towards another human being! I mean, come on, they have been specifically told to disregard Hannelores objections, even when threatened with being removed by the police (or murdered), and they agree with that??? No... Just no!
2.: Tilly adds nothing to the QC universe
Tilly is a plot device. A MacGuffin. A simple catalyst for other characters (mainly Hannelore) to become active in some way or another. Nothing more. This could have been achieved in many other ways. What if Winslow was starting to act weird? Maybe there's something wrong with his new chassis... What if Hanners had fallen down some stairs and both of her arms get broken. Now she's suddenly forced out of her comfort zone. Maybe the others try to take care of her while constantly working around her many OCDs. What happens when Mom and Dad get the news that "the heiress" is injured?
Tillys non-binary-ness is the only thing that make them stand out, but it really adds nothing to them. Go back an read the whole arc from the beginning, now that you know about Tillys preferred pronouns. Does it make any difference? Does it, in retrospect, make Tilly more likeable, or their behaviour any less outrageous?
3.: The QC cast is already big enough as it is.
The QC Wiki lists 138 pages for characters alone. This includes the ones that may have only shown up once and/or played a miniscule role - Doras cat Mieville has its own page - but nonetheless. Even if we say that only 10% of those are really part of the main cast, that would still leave us with ~14 characters to write stories for. Make that 15% and you have ~20 characters. One would think this is more than enough. Why not flesh out an already introduced character instead of adding yet another one to the QC universe?
TL;DR: Tilly reminds me of an overtly exited puppy, especially with them trying to climb over the counter and their almost insane eagerness to please Hannelore, even in the face of severe opposition. I'm sure this was done to make them look cute, but for me it did exactly the opposite. This character is broken. Even if they show some redeeming qualities in the future, I don't think I could warm up to them.
I just want Tilly gone.
Regards
Bad Supes
PS: This them/they stuff really needs some getting used to. It feel like I'm being intentionally rude to someone. Also, in german this would make no sense grammatically. The plural form of almost everything uses the female pronoun “die” (Die Gruppe = the group), with only very few male and neutral exceptions (Der Schwarm = the swarm; Das Quartett = the quartet). And with neutral I mean the plural form of "it".
I don't know how german non-binary people go about this stuff. I would assume that most of them just use the gendered pronoun they feel more comfortable with, but that is nothing more than speculation on my part. Also, the topic of sexuality, gender identity or sexual orientation is something that just doesn't come up much in an ordinary conversation. It's more of a private thing.