How to tell existing users that free features will be premium soon?

Not an email tip.

But Make it easy to upgrade. Users are far more likely to abandon their purchase if there are too many hurdles to jump over. Hope fully this helps - https://hbr.org/2014/05/making-freemium-work

I can't speak from my experience, but I'd communicate the date of becoming paid a meaningful time in advance (a month or so -depending on what is logical for your product). Also, I would offer your beta users a discount code along the news.
However, I'm curious if someone else can speak from experience.

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@dario_raijman In my experience, by doing this, you may also lose some good customers. However, you can offer special discounts to these current users, which can make them more loyal to your product because you're paying attention to their previous users. On the other hand, previous users will also have the opportunity to get your product at a special discounted price.

i would reserve for beta users a special discount like 60-70%

Good read from the replies. This is like telling my founders cafe members that subscription terms changed.