I just finished a play through of Mario and Luigi Partners and Time and here are some important lore reminders:

Bowser's fixation on abducting Princess Peach apparently started as early as when he was a toddler, suggesting this obsession is less sexual/romantic and more juvenile and/or power motivated. At least initially.

Toadsworth, in a life threatening crisis, will readily defer to literal infants to handle situations involving direct combat with invading forces.

Luigi stands in judgment before the gates of Star Hill and is implied to have multiple dark secrets that he is desperate to avoid Mario and their baby selves from hearing about. Luigi is required to go through a trial to demonstrate his soul of worthy of entering Star Hill.

(The Star door later back pedals, claiming Luigi's soul is beautiful and this was all a test, but this is only after Mario gets mad about his brother being insulted)

Professor E. Gadd pumped several kilolitres worth of CHILDREN'S TEARS into the past.

A line of dialogue suggests that these tears are synthetically created, but he still refers to them as baby tears and I would not be shocked if he just had gallons of tears on hand.

We are shown a female thwomp, who is round, has hands and does not have spikes. She is the only one like this to me knowledge.

Thwomp Volcano spits out thwomps when it erupts. It is unclear if this is part of some sort of procreation process or if the volcano is a burial site.

Bowser meets his child version. Baby Bowser is inspired by adult Bowser and swears to surpass him in terms of power and villainy.

Baby Bowser would've been permanently transformed into a poison mushroom if Baby Mario and Baby Luigi had not incidentally discovered a cure.

The game features a significant amount of involuntary transformation, including the yoob: A gargantuan alien yoshi that eats people who are turned into eggs which are stated to transform people into 'monsters' if left to hatch.

It's all a bit uncomfortable for a Mario game.

The Mario and Luigi series in particular appears susceptible to strange kinks, since vore is the central concept of the sequel Bowser's Inside Story and threw in inflation as a main plot device.

Partners in Time MOSTLY focuses on aliens harvesting people for their vital energy.

Baby Mario has an aggressive streak and often expresses himself by smashing things with a hammer when frustrated, but is always quick to jump to people's rescue.

Baby Luigi is notably braver than adult Luigi and often has to goad adult Luigi to confront danger.

Partners in Time includes no real instance of the timeline splitting and may be suggestive that is impossible to change the timeline in the Mario universe, although this is contentious for multiple reasons.

There is a scene where Egadd is inspired to create a 'hydro gusher' because his PAST self witnessed Baby Mario spitting water. The scene visually suggests that this event instantly changed something in present Egadd's brain to give him an idea.

This is most likely just the implications of time travel being barely thought about by the writers, but taking the text as it is could suggest the past changing overwrites the present concurrently. But the tidier explanation is just that Egadd was reminded of this past event.

At no point to characters from the future comment on having any recollection of any of the events of the past, such as the massive alien invasion or having met their past selves. This is acceptable for the baby characters to forget about but is strange for Kamek and Toadsworth

Also, Egadd was initially studying geology and only switched to studying ghosts because of the incidental meddling of Mario, Luigi, and his future self, which is how he became involved in the cast in the first place.

The use of time travel does not factor into the Shroob alien invasion plan AT ALL so this suggests that if Mario and Luigi had NOT gotten caught up in Time Travel shenanigans then the Mushroom Kingdom would've been destroyed.

Unless we have some convoluted Future Trunks nonsense going on off screen, this indicates that there is only one immutable timeline where Egadd MUST invent this time machine for the present as we know it to exist.

Incidentally, the last we see of Egadd's time machine is when it is used by Toadsworth the Younger to transport himself and the babies back to past permanently.

Presumably it is only used after this point for the babies to participate in spin off titles.