I wouldn't say the site itself is the 'enemy', just that as a platform it's incentives are not aligned with their audience, ie, mongers. I don't think it really poses any tangible threat to TER, its users, or its advertisers.
I don't use Tryst to find potential providers, but, I will certainly reference it when I found a girl elsewhere and she has a tryst page.
Your timeline mostly fits. TER was blocked in the US september 2017, but available via VPN, until december 2019 when it opened back up. Tryst started early 2018, so, an opportune time, but, also, around that time the industry as a whole was SHOOK by FOSTA/SESTA, so, offering an alternative was rather apt, and there were a number of sites that sprang up at that time, most of which you can't talk about on the boards here, Tryst differentiated itself by marketing itself as the non-evil, friendlier, by-hookers-for-hookers alternative to backpage/craigslist/etc. They continue that marketing wankateering to this day.
Do note that their founders have explicitly stated that Tryst will never have reviews like TER because reviews are exploitive to sex workers, and, in their blog posts about other ad sites, they conspicuously don't mention TER, but do mention all of TER's competitors, which is a good picture of who these people are, ie, petty.