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Everything that airhead says is good advice but I'd be concerned that you may have a couple more issues than just the panel.
In the photo below I have highlighted, in red, what looks to be rot at the bottom of the door where the rail and style meet. Also highlighted in blue is some bubbling of paint along this joint (this could be natural movement but given the rot at the bottom it could be spreading) as well as the swollen area highlighted in purple it all paints a worrying picture that the tenon that holds that corner of the door together could be rotting or worse.
Out of curiosity has the door started to stick recently? The margin at the bottom looks very tight, this CAN be an issue as water that gets past the rebate at the base of the frame can sit against the door and "wick" up it causing all sorts of issues. These issues can be fixed but it's a delicate "surgery". The best way to find out is to put a mirror on the floor under the door when it's open and to check for signs of rot. If you see anything give it a poke to see how soft it is. Also check the end of the tenon to see if that's spongy.
As far as the panel goes I'd be tempted to replace it. There will already be rot along the bottom edge of it that could well have penetrated up the panel and may cause issues with the rail on the bottom. By putting timbabuild or repair care on it you are dealing in moisture when it needs to dry! Replacing the panel will not be easy but it is doable.
If you do your own work on this kind of thing and plan on doing it for a while the Dryflex kit is worthwhile over a few repairs. The dry flex also keeps well in the tube so you can use it for a number of small jobs and over a period of time.
It's a no brainer for me to have the kit and I use it all summer long on rotten window cills and doors, it still seems expensive but it's so much easier and quicker to get good results.
I used 2 tubes on a 3 day job recently (listed property and the rear doors were in very bad shape). It cost me £57 per tube because I wanted it in a hurry. My normal supplier is Sealants Online, they have the trial pack for £132.
Timbabuild starter kit is around the same money but the tubes are cheaper individually. I have both systems but the Dryflex is better for all the things, I use Timbabuild in some situations but I wouldn't recommend it alone.
You might get away with using Dryflex SF which is the surface finisher that only needs a heavy duty contractors gun to work with. It seems to be the same stuff as Dryflex when I've used it.