I'd say that-depending on how her reputation on Earth Bet evolves following Gold Morning-Taylor has a better chance than most of qualifying for the Avenger Class. That being said, I also think that it would likely be a weaker manifestation of her Heroic Spirit, despite the fact that it'd have to be based off of her final moments as Khepri, due to the fact that the usual tactics of the Avenger class fly in the face of how she's learned to fight since the beginning of her legend.
She doesn't really have one for two key reasons (though I would also say more than just bet matters since you have things like the multiple earth's she stole nukes from via portals and travelled through fighting scion). First Earth Bet got totalled during gm because aside from all the direct damage including Scion opening it with wiping out all of the UK in 1 blast as a last tribute to Kevin Norton who was already dead by then, gm caused things like Nilbog's goblins and the machine army to bust out of their containment zones, a ton of stuff including tinker tech got abandoned and violently failed and people knew about the portals to Gimel so they tried to reach them.
What's left is basically just the people unable or unwilling to get to a portal, forced to stay by warlords who don't want to give up their power and the Wardens (basically reformed protectorate) who are supposedly dealing with the previously mentioned problems but left the machine army unchecked and the only time we actually saw them on bet it involved them standing around in Africa not actually doing anything about the warlords until GU came in and stomped them.
Second while writing Ward I am about 95 % sure Wildbow was determined to spite the fandom and despite his claims he never reads any worm fanfics he pretty thoroughly went about trashing the most common fanon and a lot of well liked people especially Amy. He simply hit suspiciously many for someone who doesn't read fics to the point that out of the characters who actually had stuff in Worm the only one your likely to finish Ward with a higher opinion of is Vicky. However, she doesn't really count because she's basically an entirely different character but claims she's always been like that despite said claims including things like she's always had a warrior monk philosophy and approach to fighting where she's about keeping a cool head and calm, collected and careful applications of precise amounts of force to avoid collateral damage.
Due to this approach Taylor is pretty much completely ignored and forgotten about with mentioning her basically being taboo with the most being a few indirect references or mentions in private conversation between people like Vicky and Lisa. To be fair it isn't just Taylor since all capes who were involved in the scion fight both willingly and unwillingly came to some sort of agreement to just not talk about the whole thing at all which means very few of those people know the one controlling them was Taylor specifically due to the heavy portal use and her being in costume. However, when they finally did talk about scion they still left Taylor out of it probably due to not wanting to admit to the whole having to be mastered into fighting.
It is also worth mentioning because they are on Gimel they are also busy sorting basic things out to the point that a ton of people died during the first winter due to there not being enough food and they only just got the internet back but only in the megacity and a few places around it.
Practically speaking as Taylor Hebert she is far more well known for being the warlord who took a US city, changed sides after working with the heroes to put down the Ziz bomb Alexandria (the cover story Dragon put out while the prt were reeling which was big enough even Phir Se in India knew of her from it) and being the person whose body cam footage was released for the only publicly available footage of an endbringer fight which is also the one were Behemoth died.
