Exact same thing happened to my boys bat (harrow) the other day.
Dinged the ground (concrete underneath 'carpet'?) in the nets digging out a yorker ... damage from hitting ground not ball (on video). Damage very similar to yours - just half way between centre and outside edge.
I stood some PVA glue in it overnight (level) and let that soak into the gaps. This morning the 'dent' was about half full but the cracks at the top end were bonded.
I gave it a bit of a gentle knock with the mallet just to try and compress the damaged area (not too hard ... didn't want to force open cracks again). I have just put a bit more PVA in to try and make it more level. Doubt I will do any more.
I had been going to sand an older bat into the glue to make a 'filler', but this glue is clear and as a result is practically invisible. I think that unless the willow 'shade' from the other bat had been identical I would have made more of a 'cosmetic mess'.
After that I will remove and re-attach the toe guard. It is clear based on both my and your ding that the rigidity of the toe guard at the end prevented more damage i.e. the damage is up towards the face rather than into the toe as you sometimes see. I may deliberately leave 1mm or so overhanging the face instead of trimming perfectly flush as I did last time as a small "bumper".
I will probably wrap some bat tape around the toe. Not sure why we think edge tape on vertical edges is a good idea but not the toe which is probably weaker due to lack of less pressing to start with and being thinner(?)
My son was quite sad about his bat until I showed him pictures of international players with seriously bandaged up bats so now I think he actually wants some tape