The Warlords being abolished at around the same time as Wano is pretty convenient for where Mihawk is concerned. Currently, the Strawhats are in Wano, the land of Samurai. Swordsmen like Ryuma and Oden in particular are getting hype. Indirect hype for Mihawk. Zoro himself is set to grow as a swordsman since his timeskip training.
All this, and Mihawk has kept a low profile. Until now. Relinquished of his Warlord title, Mihawk is now only defined by his status as the 'Strongest Swordsman in the World.' As written earlier, the Samurai of the Wano Country are receiving a lot of hype as combatants. But for as great as they are, Mihawk is the current WSS, and Zoro's ultimate goal. I think Oda having Mihawk on the move now is to coincide with Zoro's growth in Wano. Zoro has managed to surpass all these Wano Samurai, who have been lauded for their strength, yet he is still so far away from Mihawk.
"Congratulations, Zoro! You defeated King, surpassed all of Wano's Samurai in recent memory, landed a critical blow on Kaido (With heavy assistance), turned your sword black. However, Mihawk just casually annihilated an armada of Navy ships single handedly, whilst being reminded as the Strongest Swordsman in the World. Still got a ways to go."
This isn't the first time Oda did something like this either. Zoro was struggling to even get a nick on Mr.1 during Alabasta. It was one of his toughest battles. Fast forward to Marineford, Mihawk cuts that same Mr.1 the moment he identifies him.
In Stampede, Zoro had to cut a meteor sent by Issho. He had to use his strongest Santoryu technique for it to only be cut in half. Mihawk completely obliterate the 2 halves of the meteor with but a simple swing of his blade. Stampede is not canon. However, Oda supervised the development of the film. If he deemed there was anything that didn't align with his manga he could've prevented its inclusion. Probably why Sanji didn't get matched up with an Admiral like Zoro.