That looks like a Suntour Shimano* 6-speed freewheel, not a freehub-type cassette. With some possible respacing of the rear axle, you could get a 7-speed freewheel on the back, but not any more than 7 speeds without replacing the entire hub / wheel (even if you source an 8-speed freewheel, the rear axle is likely too narrow to accommodate without running out of threads, plus the unsupported axle length would probably result in breakage). If the Microshift bar-ends are intended for 8 speeds or more, you're gonna need a completely different cassette-hub wheel or rebuilding your existing wheel with a cassette hub (not for the faint of skill).

If the Microshift bar-end shifters are indexing-only on the rear, you will need a different rear derailleur, as I recall the Deore deer head rear is friction-only (and mildly collectible if it is removed). Not surprised it has a mismatched rear derailleur - the OEM Suntour Mountech rear derailleur was a design too far in terms of innovation - placing the spring inside the pulley resulted in crud intrusion and pulley seizing.

*missed the VIA stamping on the first glance