Hi,
44 years ago having just got married the building society held back funds from the mortgage until similar rot was repaired to our bay window. The glass was single glazed and leaded and as we were on absolute maximum mortgage couldn't get someone in so this was my first ever woodworking job.
We visited a local DIY store where we bought just enough planed timber. I bought a 3/8" bevel edged chisel and already had an hammer. I also bought a single speed B&D drill plus one of these for cutting rebates;
https://www.tooltique.co.uk/shop/vi...orrucut-rebate-and-grooving-drill-attachment/
For the moulding I simply made the new frame with mortice & tenon joints then rounded the inside edges with abrasive paper. It took a lot of patience to remove the glass without breaking it but once the new frame was in position with the original glass installed the building society inspector was happy to pass the work and the funds were then released; I did the work on an old rickety farmhouse table left by the former owner doing this upstairs in the spare bedroom. Desperation got me into woodworking and now I not only enjoy woodworking I can make anything.
These days of YouTube video's and very cheap routers such work can be carried out by a complete novice if a lot of care is taken.
To answer your question regarding making good with filler; in my experience filler of any kind will fail at some point sooner or later; do the job and do it once; a bit of timber and a few tools are cheap enough.
I've just replaced six lots of glazing still retaining the original woodwork only needing new wooden beading which I made; three single panes of privacy glass and three double glazed units saving a lot of money whilst I enjoyed doing the work.
I always recommend researching then doing the job; all those years ago I had to learn from books.
Good luck.
Kind regards, Colin.