OK. Ignore tokens and Pathfinding for a moment.
Take a look at
Trade, which is a more straightforward Event.
When you buy Trade (which you may do during your Buy phase, using up 1 Buy and $5 of your spending money just like if you were buying a $5 Card) you immediately do what it says on the card: you trash up to 2 cards from your hand and gain a Silver per card you trashed. Once you have done that, you have finished buying Trade and you continue your turn. You've trashed some cards and gained some Silvers, but beyond that nothing "continues to apply for the rest of the game".
You can buy Trade again later (even later that very same turn, if you had at least two Buys and at least $10 to spend!). If you do, you get its effect again.
That's how Events work.
Now let's look at the "+1 Card" token. If that is on a Supply pile then, when you play a card from that pile, you first get +1 Card. That benefit lasts for as long as the +1 Card token remains on the Supply pile. You get the benefit because the token is there, regardless of how it got there.
That's how tokens work.
Now look at Pathfinding. But ignore the section in parentheses.
When you buy Pathfinding, you "Move your +1 Card token to an Action Supply pile." You do this immediately, and once you've done it, you've finished buying Pathfinding and continue your turn.
Pathfinding's effect is momentary and instantaneous, just like Trade's. If I tore up Pathfinding after you'd bought it, everything would continue unaffected, you just wouldn't be able to buy it again.
It may help to compare and contrast with
Teacher. That's not an Event, it's a card in your deck, but it too can move your "+1 Card" token. The "+1 Card" token behaves identically regardless of whether you moved it using Teacher or Pathfinding.