It's not "splitting the vote" it's just an election with more than two viable options.

Say you have three major parties, the left wing democratic socialists, the moderate left liberals, and the right wing conservatives. The liberals do not generally support the more radical reforms of the democratic socialists, and the democratic socialists think that the liberal policies are too ineffectual and do not address the source of the problems as they see it. But they ultimately agree on the general direction the country should be moving and both of them know that the conservatives stand against nearly everything that they they stand for, and in fact have been recently marching towards far more dangerous policies that need to be stopped now. This should all sound very familiar.

Now, polls show that the general public's first pick for party representation have 25 percent support for democratic socialists, 33 percent for liberals, and 38 percent for conservatives, with 4 percent undecided. If everyone votes for their first choice, the left wing WILL lose and the conservative party will take control. Despite the majority of people generally on the same side, the left, they still lose. This is the spoiler effect.

So say, instead, that people that fall in the middle, politically more between the liberals and democratic socialists see the writing on the wall and decide to switch from support from the democratic socialists to the liberals to ensure they don't lose to the conservatives. Now the vote goes 16 percent democratic socialist, 43 percent liberal and 41 percent conservative and the liberals win by a narrow margin. This happens a few more time, maybe sometimes with the conservatives winning because people get comfortable voting again for the third party and spoiling the vote again just enough to lose the election for both left wing parties. Eventually, most people realize that the democratic socialists have no chance of gaining a plurality and so apart from a small percentage of hold outs, they get very few votes. Now you have a two party system. This is almost ALWAYS how this eventually happens.

BTW, if you switch to Approval voting, those people get to vote as they see fit for as many parties/candidates as they see fit. Their could be dozens of parties/candidates running, and they could actively be running joint campaigns or endorsing one another and there is no spoiler effect unless a majority decide only to vote for one and only one candidate (which would be functionally identical to First Past the Post). In the example numbers, many of the liberals would have also supported the democratic socialists and vice versa. One of the two would have won (usually the more moderate party, but not always), and the conservatives would have had to compete with their joint efforts instead of letting them fight each other to the conservatives advantage.

The coalition agreements between parties keep the third parties more active and viable for sure. And third and fourth parties (and independents) are much more viable in smaller scale votes like individual districts that leans hard away from one of the major parties (much easier to get a democratic socialist voted for in a district where the Republicans dont stand a chance and so you have no reason to worry about the spoiler effect). But even in Canada, the PM vote ultimately came down between Carney and Poilievre, liberal and conservative, didnt it?