WI: Southern Rhodesia joined South Africa in 1922?

In 1922, there was a referendum in the British colony of Southern Rhodesia (later Rhodesia, now Zimbabwe) on whether or not to join the Union of South Africa. In our timeline, they decided not to, but what if they did?

Specifically, what would happen to Bechuanaland (modern Botswana), which would be completely encircled by South Africa (because they also owned Namibia at this time). Would it become a bigger Lesotho, or would it also be annexed to South Africa? What about Northern Rhodesia (modern Zambia)?
If the Rhodesians vote for the United Party, then you'd avoid a National Victory in 1948 and thus avoid Apartheid.

Bechuanaland would be completely surrounded by South Africa with the teensy exception of the Quidripoint. But if Swaziland and Lesotho weren't annexed OTL, why would Bechuanaland?

South Africa would have a liberal immigration policy with regards to people from Central Europe (as the United Party Planned to do OTL before losing to the National Party). You'd see greater rights for Non-whites including some indirect democratic representation IIRC. By the 70s or 80s that might liberalize to something closer to majority rule.

You'd see a richer country to without Apartheid. Holding back large parts of your population tends to not be good for economic well being. Plus there were certain structural economic limits (ergo, if in a 85% black country it is illegal to promote people based on race, that tends to limit how big or productive your firm could be).