It's a bonkers transfer strategy. You broke your transfer record for Keita, only to agree to let him stay in Germany until next September, knowing full well that CL qualification was far from guaranteed this season, and that your best player could well be leaving before he gets there.
You spent all summer refusing to break the bank for van Dijk, only to do so halfway through the season.
It's not really about getting close to City because they're not really a fair yardstick to be using. You're currently closer to Arsenal in 6th than you are Chelsea in 3rd, and fell at the first hurdle in one of the two more winnable competitions you get to enter every season. Bringing in Keita for this season and spending this money on van Dijk in the summer may not have closed the gap on City in any meaningful way, but signing Messi was unlikely to do much in that regard either.
You talk about the possibility of van Dijk signing in August meaning you'd have 4 more points from turning draws into wins, which doesn't sound like much, but it'd put you 5 points clear of 5th, and in the mix with United and Chelsea for 2nd, rather than Arsenal and Spurs for 4th.
As an aside, you can only beat what's in front of you, but winning a group that contained two of the bottom four ranked teams in the competition hardly constitutes a roaring success. Before the format reshuffle Spartak Moscow would have been in Pot 4, and actually ranked lower than Maribor.