AskVibeNot tax advice, but the practical picture:
Stripe Tax calculates and collects the right VAT at checkout. It does not file or pay it. You're still the seller, so you'd register for OSS and file a quarterly OSS return with the amounts per country. It's one return, not 12 registrations, but it's on you.
A Merchant of Record (Paddle, Lemon Squeezy, Polar, or Stripe's own Managed Payments) legally resells your product. They're the seller to the customer, they handle VAT everywhere, and you invoice them. Typical fees are around 5% + 50c per transaction vs ~1.5-3% + tax work with plain Stripe.
The €10,000 rule: if your total cross-border B2C sales to other EU countries stay under €10k per year, you may charge Dutch VAT on everything and skip OSS. Above that, destination VAT applies.
KOR: if your total turnover is under €20k you can opt into the Dutch small business scheme and not charge VAT at all. Check how that interacts with foreign sales with an accountant.
For "I'd rather pay a few % than do paperwork", a MoR is exactly built for you. At €7/month the fixed 50c hurts a bit, so consider pushing yearly plans.