7 teams will start tournament directly from part 2 (7 is odd number, part 1 will be skipped), were they must play each with other, thus 21 games will be played instead of 7, meanwhile 8 teams will 4 quadfinals, play 2 semifinals, 1 final = 7 games, just much as you need. So, here only one correct answer: 8 teams.

Second case is the same, 67108863 teams will play 2_251_799_713_021_953 games, instead of 67108863.

Tests do not seem to be working.

Failed when n = 7: expected [ 7, 8 ] to deeply equal [ 8 ]
Failed when n = 67108863: expected [ 67108863, 67108864 ] to deeply equal [ 33558528, 67108864 ]