need help with domain transfer

Although I have been on Squarespace for years I am transferring to a platform that has more robust portfolio features. 

Square managed my domain (using Tucows I believe) 

 

Following your forums I have taken these steps:

unlock domain 

request transfer confirmation code

receive transfer confirmation code

in advanced settings I have transferred to option:  custom nameserver 

now when I use my url I am taken to my new provider 

 

It is unclear to me what my next steps are. What to do to have my domain registrar transfer.

Send the domain transfer code to my new provider

transfer domain from Tucows/square to namecheap (the domain registrar my new host uses) 

edit DNS records - remove

 

I’ve been scouring the forms about this topic and continue to be confused. Hopefully you can help clarify.