Does this download include any privacy incursion functions, such as contact tracing?

iOS 13.5 does contain the API that allows contract tracing to work. If you are that concerned about it, do NOT upgrade. Bear in mind, you will be stuck at iOS 13.4.1 now since I assume that all further upgrades will contain this ability to use contact tracing apps.

If you are worried about being tracked, you have no idea. Read the reply form Lawrence Finch in this discussion. His answer should open your eyes if you are worried about being tracked.

How to remove iOS Update notification badge for COVID19 update?

This applies in the U.S. and it may be even worse where you live.

Re the new download that is available... does it include any privacy incursion functions such as contact tracing?

New download" is pretty vague. Assuming you mean iOS 13.5.

iOS 13.5 includes the underlying code that should you choose, will allow an app that you download at a later date, to offer some level of tracing.

Since those separate apps do not yet exist, it is impossible to know how they work and what they will track or trace.

The actual tracing app is entirely optional. Using iOS 13.5 does not mean you are using an app that tracks or traces you.

It can't be explained more clearly than that.

iOS 13.5 contains no tracing software. It does contain the API for authorities to create an app capable of tracing those users that wish to use the capability.

If you can refrain from downloading that very specific app, you will be fine.

If you can refrain from activating the tracing app after downloading it, you will be fine.

I don't believe it answers my question as to whether or not this most recent download alert contains the contact tracing function in it.

Do you understand now?

It's been explained multiple ways.

The FUD around this is asked about every day and it will be helpful for us going forward if you indicate that we are explaining it in a way that helps you understand.

See: Privacy-Preserving Contact Tracing - Apple and Google