So, the way I'd handle Talia and Selina in my take on the DCU is
The first time they meet is when Selina steals a thing from someone who - unbeknownst to her - is part of the League of Assassins. One thing leads to another and Selina ends up fighting Talia. Talia's the better fighter but Selina's fighting to escape not to win so she's able to get the upper hand just long enough to get away with the thing she stole. All this would take place away from Gotham
Some time later, the League of Assassins does track the mysterious thief to Gotham and now Catwoman's dodging assassination attempts from ninjas and there's Talia. Selina manages to beat most of the other Assassins fairly easily, but Talia's more difficult - but Selina's also a con artist so eventually she's able to trick the League in a way that makes it clear that they do not want to mess with her. Talia is actually impressed
After that, there'd be a pattern where any time Selina tangles with the League of Assassins, she also tangles with Talia. The two develop a very strong and increasingly homoerotic rivalry
[As an aside, my take on the League of Assassins leans very much into the "cult of personality around Ra's" version.]
[As another aside, while this post isn't about Bruce, I will say that when Selina and Talia first meet, Batman and Catwoman have had an ongoing flirtation for a couple of years and Bruce and Talia have known each other for maybe a week and have some sort of affection for each other already]
Once they've been solidly established as rivals and enemies, that's when they find out that they're also both romantically interested in the same vigilante.
Over time, we get subversions of that rivalry. Situations where Selina and Talia have to team up for various reasons. That does include a similar set-up to The Brutalina Issue, but also situations like "the League of Assassins needs to steal a thing and Talia decides to recruit Selina for it" or "Selina and Talia are going after the same target and decide to work together" or "Selina needs ninja assistance for a caper and decides to call in a favor Talia owes her"
During one of these team-ups, Selina insists that they absolutely need to have a Girls' Night Out. Hang out, get drunk, party, talk about boys. Also girls. If you're into girls. Are you into girls, Talia? Not that Selina's interested or anything, she just thought it would be worth asking. For reasons
Subtlety in romance is not Selina's strong suit
After that, Selina and Talia do begin to develop a romance, and this is where their relationships with Bruce become a bit more relevant. Because yeah, all three of them are happy with polyamory, but. Ra's is kinda weird about Talia's and Bruce's relationship, and. Well. He's unlikely to react well to Talia having a girlfriend on the side, especially one who's a thief, and especially a thief who is also dating Bruce, and Talia knows that and worries for Selina's safety. It's a whole thing
The details get hazy after that but I do know that Damian and Helena both come into the picture at some point, that at some point Talia gives Selina some ninja training until Selina is actually able to match Talia in combat, and that there's definitely some sort of polyamorous situation going on with those two and Bruce but I'm not sure of the specifics
Also, at some point post-ninja training, Selina and Talia kick Ra's' ass together, though Talia is the one who actually lands the final strike
