It’s flawed data though. City faces PL teams later in the competition when the non-PL teams are already eliminated. So they are getting PL teams when they can only draw against PL teams.
Liverpool is 66% because it is 18/27. City has played twice as many games because they get to knock out the minnows.
Also because Liverpool went out to the relative minnows. In their first couple years, Liverpool was eliminated by West Ham (7th - PL), Wolverhampton (CH), Southampton (8th - PL), West Brom (20th - PL), and Leicester (9th - PL). They were also nearly eliminated by Exeter City (L2), Carlisle United (L2), Stoke City (9th - PL), and Plymouth Argyle (L1). After the 15/16 EFL Cup final, it wasn't until 2018's EFL Cup where Klopp was eliminated by a team that finished 6th or better in the PL.
Let's go year by year to where a team was eliminated.
15/16 FA Cup -
Liverpool was eliminated by West Ham in the 4th Round having faced 1/2 PL teams. City through the 4th Round faced 2/2.
15/16 EFL Cup - Liverpool lost to City in the final; Liverpool played 4/4 PL teams,
City was 3/4
16/17 FA Cup -
Liverpool lost to Championship side Wolves in the 4th Round having never played a PL team; City had played 2/2
16/17 EFL - City lost in the 4th Round to United (2/2 PL);
Liverpool had played 1/3 PL teams (and would go on to play another CH side before losing to So'ton in the semis).
17/18 FA Cup - Liverpool lost in the 4th round to a West Brom side that would get relegated (2/2 PL);
City was 1/2 PL sides there.
17/18 EFL - Each played 1/1 PL sides when Liverpool went out to Leicester in the 3rd round.
18/19 FA/EFL Cup - Liverpool lost both their opening round matches to Wolves and United;
City had played no PL teams at the point
19/20 FA - Liverpool went out in the 5th Round (2/3 PL);
City (0/3 PL)
19/20 EFL - Liverpool (2/3);
City (1/3)
20/21 FA - Liverpool (2/2);
City (0/2)
20/21 EFL - LIverpool (1/2); City (1/2)
In total that's 18/26 PL teams for Liverpool (69%) vs. 13/25 for City (52%). Of course, if you only go until 18/19, that's 11/16 for Pool (68.75%) to 11/15 for City (73.3%). To the extent it's a conspiracy, it's lasted all of two years, and if you cherry pick 2 years (say, Klopp's first two years), you can make it look like Pool was the beneficiary (6/11 Pool; 9/10 City).