I am no expert but I have come across this situation with other email providers. How close to or far over the limit are you now? You can't decide what to do without this information.
If you really can't delete anything then you will have to set up another email address for future emails and make sure you keep enough space in your existing account to cater for things like recovery emails or important things. You can change the recovery emails to a new account.
Very often emails with attachments are the biggest space hogs. Order your emails in attachment size order. Probably the attachments are already or can be stored elsewhere and then the emails deleted.
Do you do online shopping? This generates a lot of emails. Do you really need to keep most of them, especially the older ones? Select the main companies you shop from and you can probably delete most. Likewise bank, paypal, shopify notifications. If you have registered accounts with companies you can usually find all your order histories there you don't need the emails long term.
I think some providers offer a facility to to export/download your emails and then you can keep them in a folder in your documents file. See if Yahoo offers this. Edited to add - You can then delete the emails from the Yahoo account.
If you want to keep using your yahoo account you will have to delete something if you are over the storage limit.
You can set up another email account, including with Yahoo and use that for eg shopping or whatever your main email traffic is for. Then keep the existing account for friends, family.
Yes, it is a pain and Yahoo are making a lot of work for their customers. But I am sorry to be the bearer of bad news that if you are close to or over the storage limit you will need to do something. I don't think there is any solution that doesn't involve some combination of deleting things and/or setting up a new email address. If you stay with Yahoo you will have to make sure you stay within the limits.
A friend of mine was notorious for going over the limit on her account and then no-one could get in touch with her. Or not by email!
Good luck.