best substitute for Entourage as mail program?

Forgot to mention something rather important.

You cannot import Entourage data into Office 2016 or newer. It must first be imported into Outlook 2011. This is the only older database Outlook 2016 or newer will read in an automated fashion.

It is possible to bring Entourage data into Outlook 2016, 2019 or 365, but it all has to be done manually.

If you want a monlithic app similar to entourage, that would be Outlook.

If you want a simple email client that isn't bogged down by a bunch of useless dreck, there are many available. There are also many in-between.

Every email client can handle multiple email accounts.

Search the App Store or the web for "email client" and pick from the one that seems to provide the features you want.

Some are available for free or trial period.

You will probably find many specifically written for Gmail because Gmail isn't really a standard email protocol. The rest should work for any standards-compliant (POP, IMAP) email accounts.

The monolithic database of Entourage and the initial release of Outlook (Office 2011) is gone as of Office 2016. There isn't even a Database Utility anymore because there's no need for it.

All emails in Outlook 2016 and newer are saved as individual files, as are any attachments. Anything removed from the Deleted folder is instantly gone. There's no need to run a utility to get them out of the older style database.

If an email does somehow become corrupt, it will be only one damaged since it isn't connected to anything next to it. The new process also eliminates the 2GB limit of the old database. You can have as many emails as your drive can hold.

There are definitely other good choices. I focused on Outlook since the OP stated they liked the way s/he can organize mailboxes in Entourage by topic and the fact that I can download mail from my multiple email addresses. Sticking with Microsoft's Outlook makes the transition to a new email client as seamless as possible as it will behave almost identically to Entourage.

You would have had to purchase the Business version of Office 2011to have Outlook included.

Though I guess I have to ask how you got Entourage in the first place if even your copy of Office 2008 doesn't have it. Is it from Office 2004? If so, I'm kind of surprised that even runs in Mojave.

By far, the easiest way to move forward is to first import the old Entourage data into Outlook of Office 2011. If you know anyone at all who uses this version, have them import your data to a new user account (so your data doesn't get mixed with theirs). Then take that converted 2011 Main Identity folder to your Mac and import it into Outlook 2016, 2019 or 365.

I tried to find a trial version of Office 2011, but there isn't such a thing.

I would imagine you can still purchase Office 2011 with Outlook somewhere, but it may also be pricey for a one-time purpose. Legal copies from stores run anywhere from $100 to $219. eBay is a better bet for cheap and legal. Lowest I saw currently available is $25 for a used copy. You only need it once, so the cheaper the better. $30 for this one. There is someone selling download only copies for $15, but you know those are illegal. I wouldn't touch that with a 39½ pole.

But before you do that, see if you can export general data out of Entourage. File > Export. Check everything you want to export. I believe it creates a .olm file. See if you can then import that into Outlook 2016 or newer.

I also found a post of mine from a bit over two years ago that may help:

Found a site where you can download the full Office 2011 installer. You should be able to run it in demo mode long enough to import your 2008 data so you can get that into Office 2016.

I cannot vouch for the safety of files downloaded from this site. Proceed at your own risk.

For a reasonably safe method, make a complete and restorable backup of your system, first!

Install Office 2011 and import the 2008 data.

Copy the converted 2011 Main Identity folder to another drive.

Restore your system to remove any and all changes made by the 2011 installer.

Copy the 2011 data back and import it into Office 2016.

Just about any email client will do as you described. Try them and then decide which is best for you.

Some time ago I checked around and settled on Thunderbird. It is also free. As noted in the comments above most email apps are now somewhat similar in what they can do.