The Pipe House theme from Super Mario RPG also known as Mario’s Pad is a combination of Mario Bros 3’s Grass Land theme and the iconic Mario Bros 1 Overworld theme. A remade version of that same song was used in another Yoko Shimomura composed Mario game and its remake. It’s the World Map theme from Mario & Luigi: Superstar Saga
https://www.youtube.com/watch?v=Of3f3LMKFig
https://www.youtube.com/watch?v=CrRK1g_F8C0
https://www.youtube.com/watch?v=1dkE3boAJRo
From Inside the Earthern Pipe from Super Mario RPG is the classic Underground theme remixed with some more synth ambience to it. A remade version of that arrangement appeared in the first Mario Party game as The Room Underground.
https://www.youtube.com/watch?v=iJHnjs_AO1s
https://www.youtube.com/watch?v=wSRYXV4_n38
Bowser’s Magma Mountain from Mario Party starting at 0:23 uses the same organ melody from the first and second visit of Bowser’s Keep from Super Mario RPG. (The beginning also reminds me of Pokemon’s Indigo Plateau and Earthbound Beginnings/Mother’s Mt. Itoi music)
https://www.youtube.com/watch?v=1hcX2bVB5ew
https://www.youtube.com/watch?v=E1ZzAv7MVeA
It might seem like an original composition at first but I think what justified it to be used is that starting at 0:30 it begins to transform into the Bowser boss theme from Mario Bros. 3 which also got used in Super Mario RPG.
Speaking of which, the Smash remix sounds like the transitions between the parts are at least partially inspired by the Super Mario RPG version with some guitar riffs of his boss music in Yoshi’s Island and then a section remixed after the Dark Land theme from Mario Bros 3 which was also the base for his Mario World boss theme. So it really is a medley of many great parts of Bowser‘s history.
https://www.youtube.com/watch?v=dlY1kw8u22w
https://www.youtube.com/watch?v=ocAJZWp40Y8
The last one is Peach’s Castle from Fortune Street which is a remade version of Hello Happy Kingdom from Super Mario RPG. This one is a song not based on any of Koji Kondo’s works but an original composition of Shimomura so likely a song under ownership of Square Enix. This might explain why it was used in this game as Fortune Street was developed by Square Enix. The Fortune Street arrangement was done by Koichi Sugiyama, the famous Dragon Quest composer.
https://www.youtube.com/watch?v=JjZQV-3GS2A
https://www.youtube.com/watch?v=wH6xr-e_jcY
Also of note is Yoko Shimomura’s Memoria compilation album which featured many orchestral arrangements of her older works including Super Mario RPG’s famous Forest’s Maze at
00:03:36 and Goodbye Geno at
00:45:46 and was published by Square Enix, finally confirming the ownership of these songs.
https://www.youtube.com/watch?v=wURsjrwX0Rc