From Wiki
The Act gives people with gender dysphoria legal recognition as members of the sex appropriate to their gender (male or female) allowing them to acquire a new birth certificate, affording them full recognition of their acquired sex in law for all purposes, including marriage. The two main exceptions are .... etc etc
People present evidence to a Gender Recognition Panel, which considers their case and issues a Gender Recognition Certificate. If the person involved is in a legally recognised marriage they will be issued an 'Interim Gender Recognition Certificate.... etc
The Act requires applicants to have transitioned two years before a certificate is issued........ Successful applicants are entered onto a Gender Recognition Register, held by the registrar general, similar in operation to the Adoptions Register for those who have been adopted. (my emphasis)
So there is a legal procedure to go through. It is not as onerous/ stringent as the process you describe for adoption because an adult is making decisions about themself. For adoption there are 2 parties involved and a baby cannot represent him/ herself.
The "biological function" of motherhood is not simply passed from one person to another by being "redefined".
Where did that come from? We're not talking about passing on functions from one person to another.