Horyuji

Hello, I am planning the following plan for 15th August:

Depart from Kobe and leave my baggage in Kyoto station.

From there go to Fushimi Inari and just take a picture of the toriis - no further walk - I've been there before and it should be fast.

After that go to Horyuji and visit it.

After Horyuji go to Nara Park and Todaiji and Kasuga Taisha (they are open late that day because it's obon festival in Nara and they will close late)

Come back to Kyoto, is it doable this plan or too rush because of Horyuji? Thanks

It's certainly doable, though a fair amount of time will be used in getting to and from places. Daylight hours are also still quite long in August.
Fushimi Inari is literally across the street from the JR station, so that will help. Getting to Horyuji is a bit of a chore. I walked from Horyuji Station and it took about 25 minutes, so not too bad. It is actually quite a huge complex, but most of it is off limits to the public. It has some extremely old buildings and structures, but its real prize is the art in its museums. Normally I don't spend too much time on such things, but some of the artworks were simply extraordinary.