I've tried to login to one of my other shops to update my new phone number, only to be hit with requiring a Security Code to be sent to my old number, which I have no access to. How am I supposed to login to change it with the constant loop of needing a security code to login? It's not this account.
Use one of your backup codes that you received when you signed up.
@KizzieEmbroidery: "How am I supposed to login to change it with the constant loop of needing a security code to login?" If two factor authorization (2FA) is enabled on that account, you can use one of the backup codes you were offered at the time you enabled 2FA.
Unfortunately it would be a major security issue to allow a change to the phone number without access to that original number, so you will need to contact Etsy to have them "delete" your old phone number.
To contact Etsy, try https://help.etsy.com/hc/en-us/requests/new?segment=selling or https://help.etsy.com/hc/en-us/requests/new?segment=selling#issue_sell_manage_listings-callback or you can open a support ticket through Dashboard > Community & Help > Contact Us
Thanks for the info. I don't remember receiving any backup codes and there is none in my emails. I'll have to try and get them to delete the old number, or try the help link above, because I can't use the dashboard contact as I can't login to the account.
the codes show up on the screen, when you set up 2FA
there is an option to download them, or print them
you have to do one or the other