It is not "government funded". This sounds like a kind of grant. Or like trans people becoming GRS money over the counter for saying "Hi, my name is Trann". It is medical expenses paid by money from income taxes, which lost of tax payers pay for all those who have medical issues (including themselves).
When we get GRS expenses paid by health systems we are getting our share of the tax money like everyone else, and not a special treatment. Just the same like everyone else, with the exception of the thorough gatekeeping and the play "hey, get dressed and prove you're a woman for about a year".
I'm saying all this because GRS expenses covered by national health systems are among the first targets by politicians claiming to have the solution to expensive health systems, turning to all possible jingoes about just sex and how unnecessary or low priority GRS treatments are. In some European countries they have succeeded.
If they give you a titanium hip because it is cheaper than paying for you sitting the rest of your life on your couch or on a wheelchair, they can give you your hormones and your parts because it's cheaper than having you depressed, drugged, long-term psychologically treated, jobless, abused, beaten, raped and killed, all of which generate some expenses for the tax payers as well.
Same with fertility treatments. Same with pregnancy care. Same with psychiatric and psychological care for old and new DSM labels. Same with physiotherapy and substance abuse rehab care. Same with millions of prescriptions and pre-emptive diagnostic treatments that keep the medical machine running financially. They're not all urgent, immediate life-saving treatments (only in the long run), but above all but money-saving treatments.