Should I make my web server Highly Available ?

If you are using XA on midrange  then connect to just one queue manager, because  anything else is not supported.  If your connection goes to a different queue manager, then it cannot recover a unit of work.

The only exception to that rule is if you are connecting to a QSG on z/OS. When using a QSG, all of the queue managers in the QSG can resolve each others transactions – this means that the transaction recovery issue goes away.

Be careful using multiple queue managers.

For the listener you want to connect to just one queue manager.  If you have a choice of two queue managers, all threads may connect to QM1, and there be no connection to QM2.  If you have a second web server instance, this may also connect to QM1, and not QM2.  It is better to have WS1 connect to QM1 and WS2 to connect to WS2 – so called production lines.

If you need to shut down QM1, then shut down WS1,  do not try to cross wire it

For the MDB logic connection factory if you had two possible queue managers, you may get a spread of connections, from all on QM1, to all on QM2, or a mixture.

If the WS frees connections (for example they are idle), then when there is a load needing more connections, it could get a connection from QM1 or QM2.

All in all – keep it simple,  and have each web server connect to just one queue manager.