Just a bit late to the party here, but I can confirm a Birmingham to Malvern Link ticket would indeed cover you via both Bromsgrove and Kidderminster.
Which bit in Worcester do you actually need? Your post didn't make that clear. I'm assuming you've done the link between Shrub Hill and Foregate Street, and the link heading north out of Shrub Hill around the eastern side of the depot, and just need the curve around the west side of the depot into Foregate Street. If so, that is incredibly easy to do.
Depending how keen you are to do the effective single line section to Henwick Crossing (ooh that reminds me of something I've wanted to do for a long time, getting a photo from that crossing, and I'm in Worcester tomorrow), then yes you'd need to go to Malvern Link. Not a bad thing, it's a nice little station. Great Malvern is nicer, it must be said, and Lady Foley's Tea Room on the Up platform at Great Malvern is worth a visit.
As for track coverage, I'm not really into that these days. My last new bit was Kraków Airport into Kraków in January 2020!