>>15692941" to 1.125"
https://www.amazon.com/Ritchey-Tom-Slick-MTB-Tire/dp/B07BYZ68K9https://www.bike24.com/p2194349.html?menu=1000,2,103,104https://www.performancebike.com/continental-gatorskin-mountain-bike-tire-26-x-11-8-0118365/p1202379?v=326306However speed advantage from 1" over 1.4" or 1.6" is minimal and high pressure slicks aren't usually that puncture resistant, so you might be better off with some average thickness slicks or even put 26" gravel tires in 2.1" on your mtb.
You might also consider to change the wheelsets, like in putting 650B or 700c road wheels with the fitting tires on your old mtb. Costs a bit more but should be faster than mtb on slicks. Pic related mtb with 700c road wheels.