@Ominous @Liquidxlax and to all others who can't understand the difference between time travel and travel to alternate realities and caused this series to catch an isekai tag:
if it is Isekai there is LITTLE TO NO interaction between MC's home and story land beyond gods doing godly inter-universal things and the occasional, and usually one way travel, between worlds. exceptions to the one way travel rule do exist though, like Ms Saving 80000 gold coins or near the end of the familiar of zero, but the two worlds are actually different worlds
if it is time travel then it is literally the same world just a different date and falls into one (or rarely two) of three main sub-types:
1 - the alternate timeline, which is borderline isekai but technically the same world when MC arrives, where changes effect the new future but MC's original timeline stays intact (to use a well known example, it's like with Trunks and the androids/cell in DBZ)
2 - the single flowing timeline where travel between past and future(s) is fairly common and changes to the past directly effect the future(s) (like in chrono trigger where for example certain events in the far past change the dominant species in the present if you return without fixing things...don't wanna be too specific cause spoilers, but this IS the category Inuyasha falls into, most notable proof being the Noh Mask event in the present) NOTE: mere shifts in the balance of powers present in the world do not make it a different world, especially when gaps of hundreds, thousands, or even millions of years between time periods visited are known to exist. if time has continuity between events in year a and events in year b, it is NOT isekai
3 - the SAME WORLD reincarnation story where MC dies and gets reborn, sometimes in the past (and if so, it is also one of the previous two categories), but usually in the future, of the same world so it's not isekai but is reincarnation and also time travel (sometimes merely a few months or a couple years, sometimes centuries/millennia) ...Inuyasha touches on this category but a: Kagome is MC the whole time, Kikyo's story is important, but she's not MC and b: due to certain events it's shown that Kagome =/= Kikyo so in the end, in spite of their connections, they aren't actually the same person, I'll admit it's close enough to really just be personal call after reading, but having watched and read the series multiple times, in my opinion it's not (it's more of a temporary ride along thing than proper reincarnation...) but even if you feel it is, this is still just a time travel category and NOT an isekai