From Derby why are you considering taking the M42??
A38 will be far easier, you will sit in traffic for hours on M42, to effectively bypass Birmingham and approach from the east rather than go straight in
A38 gets you straight into the centre atraight to the NIA and most traffic will be going the other way at that time of day, it’s a decent road all the way, gets upto 3 lanes as you approach spaghetti junction now they have ditched the bus lane, few traffic lights but it tends to flow okay. I have done Birmingham from Derby at this time of year after work (leaving around 5ish) a few times to go Xmas shopping at Bullring/German market and it’s generally been fine, generally straight to car parking around bullring/mailbox with no hold ups (apart from getting out of Derby obviously)
Jewellery quarter is easy to get to from A38 and signposted too so if that’s where more local people are saying to park I’d say go for it
(Last time I was in The Rose Villa it cost me £1500 in diamonds 😉 )