I can hardly see the technical possibilities that would allow censorship at the level that Article 13 is intended to be: mainly to copyright everything down to the last meme. If you're a content producer and you're in EU and IF article 13 is implemented the way it is considered now then there may be serious consequences for content producers and some content for sure will be blocked by whatever agency they establish to achieve that. But as I said, I can hardly see that happening.
Then again, IMHO there's a reason why VPNs are becoming more popular each year. Lots of people are skeptical about them with all that "I've got nothing to hide" but it's more about marketing than criminal activity. Browsing histories of millions of users in the target location are worth a lot and VPN adds an extra layer of protection, first of all by masking your IP address. Then there's encryption and all that stuff but to get back to your question I think VPNs will become more popular in EU because censorship is going up, and there will be a need to bypass it just like now people are bypassing geo-blocks. TBH check it for yourself, I'm using Surfshark and it costs like 1.99$/MO, there's money back guarantee in case you don't need any of it. But try browsing without any protection, see how it affects the ads, then do a week with VPN on and clearing cashe/cookies, try accessing geo-blocked content, I find it worth those few extra bucks.