I see this thread is still active.
If you have no particular OS in mind and you want new phone in June, then why not wait and see if the prices on A53/A73 come down, I reckon A73 should have better CPU?
Either way, SE design and battery life are just crap in my opinion, Im not a power user but I could barely survive with 12 Mini's battery life and now being XS user the battery life is even worse, cant imagine how crap of a battery is in SE.
If you decide that you want iPhone(my reasoning for getting iPhone for the first time was OS updates, somewhat better privacy and small size, so I got 12 Mini) then, again, wait till June, see what the prices are and get yourself iPhone 11, 12, or 13, depending on price and availability in your region.
If I had to get an Android in coming months, for me it would be either one of the Samsungs mid-tier offerings in the form of A52s/A53/A73/FE when on sale or, perhaps rumored Pixel 6A or upcoming Osom OV1 which comes from Essential phone makers.
If I had to buy a new phone now, I would see what iPhone I can get below 750$ or just get A53/A73 with Samsung buyback/freebies offers and be happy user for 2-4 years depending on how capable the CPU inside one would be.
Good luck with your choice and happy hunting!