What matters more to you - avoiding the awkwardness or getting a genuine read on compatibility? The thing is, you're already doing the hardest part right by actually thinking about this instead of defaulting to old scripts.
The people above nailed it: directness beats everything. But here's what I'd add - pay attention to the actual person in front of you rather than what you think dating norms are. Some folks grew up in households where splitting felt normal, others find it awkward regardless of year. The discomfort you're picking up on might not be about 2026 expectations at all; it might just be her personal dynamic. One woman's "let me get half" is genuine independence, another's is polite deflection because she wasn't ready for the bill conversation yet.
My take: on a first date, if you want to pay, just pay cleanly without making it a referendum on modern dating. No performance, no "I insist" battle. Then later, when there's less first-date tension, you'll naturally figure out what works between you two. You'll know pretty fast whether someone actually prefers splitting or just felt obligated to offer. The conversations get easier once you're not both running a script.