What are the chances of forming a new minority government?

Very slim, unless the far-right - centre-right collaboration fails so spectacularly that the Liberals bolts to the left again.

The 2018 election results were in raw numbers was very similar to this one. To quote myself from January 2019:

For practical purposes the parliament can be divided in far right (Sweden Democrats, 62 seats), conservative parties (The Moderates, 70 seats, and the Christian Democrats 22 seats), the liberal parties (the Liberals, 20 seats, and the Centre, 31 seats) the cabinet parties (the Greens, 16 seats, and the Social Democrats, 100 seats) and finally the left (Left party, 28 seats).

What has happened since is that after the 2021 Midsummer crisis the Liberals has gone to the right instead. They are not very comfortable there, and the Sweden Democrats at one point did threaten to bloc a cabinet if the Liberals are in it (but then again the Sweden Democrats change there position easily whenever the leadership so desires).

In this election far right + conservatives + Liberals gained a total of two seats, for a 176-173 majority.

So if the Liberals gets dissatisfied with how much influence the Sweden Democrats gets, they can bolt and a new minority government on the left can be formed. But right now, that looks very unlikely.