Well battery shapes will be custom, but the regulation does include demand to offer said batteries as spare parts.

shall ensure that those batteries are available as spare parts of the equipment that they power for a minimum of five years after placing the last unit of the equipment model on the market, with a reasonable and non-discriminatory price for independent professionals and end-users.

This being EU, EU will actually even police that reasonability clause via consumer protection agencies. You might not like the still probably pretty hefty price, but outright monopoly price gouging will not be allowed. Atleast not with in EU jurisdiction. Also makers will tend to gravitate to number of pretty standard battery sizes and geometries. Simply out of economies of scale. If you have to offer the batteries available as spares. You don't want to offer 150 different battery models on you warehousing and supply to your retail stores. You want as few as possible. Maybe say 5 different sizes or maybe couple ten different kinds on the biggest makers with the largest product range. Cheaper to buy more of similar batteries from battery supplier, than have custom module developed for each new phone model. Well unless one is apple and only has couple new models per year. They probably will have now just little bit different optimized shape battery for each models, but they also have the scale per model to make sense for that.

also:

Software shall not be used to impede the replacement of a portable battery or LMT battery, or of their key components, with another compatible battery or key components.

Meaning companies can't use software locks to deny third party batteries. Since the language says compatible battery, not replacement battery. Which wouldn't make sense anyway, since replacement battery would be the one the OEM offers. Ofcourse I'm sure there will be lot of hurdur by makers over "don't use third party batteries, those aren't as safe" and "well but that isn't compatible". However as one remembers during the early 2000's and upto mid 2010's there was a very healthy both OEM and third party replacement battery market. As with that experience, yes shoddy batteries from non-reputable people can be problem. However in this basic consumer electronic safety regulation (aka you can't just shovel anything to the market with utterly nuts unsafe circuitry in the first place) and the market itself handles it. Again it will be found out over little time, which makers are the reputable ones with the good batteries with all the proper safeties and good production quality. Reputable big chain electronics dealers then focus on only offering the established reputable third party batteries and parts out of their own reputation (You sold me a shoddy battery. It burst and ruined my phone. I'm never buying from this phone store ever again). Plus same with the actual makers with stuff like offering extensive warranties, warranting the replacement of the device, if their battery messes it up and so on.

This is all "we have already been here" ground except instead of the T9 numpad on the phone front, there is now a whole front covering touch screen on it's place.