Let's start with the basics. In SX-50 land, you can install a 2-port Auto Attendant on an analog line if you have the ports available. One of the least expensive devices is the Call Managment Products CMP Call-Extend box. It finds its way into many a smaller property because Mr. Patel insists on buying it. It's relatively inexpensive, about 1/4 the price of the COV voice mail sytsems we're talking about and you already know why you would want one.
You could buy a Panasonic 2-port VM/AA for about the same money, but that's also another thread.
https://www.callmanagementproducts.com/prod03.htm
gets you to the product.

The reason for using COV extensions in an SX-50 is because Mitels aren't very smart when it comes to handling calls. In a perfect world, your call is answered by the AA, transferred to a room and if the room answers, the AA hangs up.
What if the room is empty? Now the AA answers, transfers the call to VM and the caller can leave a message. If you use an analog voice mail, the system would have had to stay with the call the entire time, because analog integration is very poor in an SX-50.

With COV, the AA gets the call, sends it to a room, and hangs up. Thirty-six seconds later, that no answer call can ring a different port and it will know that this is a recall from NoAns condition and play the appropriate message.
The holding time of the ports is just what it takes to get the information, or record the message, or retrieve the message. It spends no time listening to ringback tones or waiting for the called party to answer.

As long as you're going to keep the SX-50, there are at least 2 companies that make a COV voice mail system. The COVoice claims to be the "licensed" vendor of the COV Mitel integration and it's the higher priced of the two systems. If you add PMS, it will cost you more that what you expected. It only comes new in 4-port increments, and when you get to a system of this price, it's both AA and VM. When your PMS send a code to clear the room, it does exactly that; all messages are erased, and there is no oops key. https://www.vsrusa.com/html/hospitality_sollutions.html gets you there.

The second COV is made by a company called DuVoice. It's probably the one you were quoted before as it is a little less expensive than the COVoice. They also have a PMS interface and are located here https://www.duvoice.com/documents/brochures/ss_dv2000-dv4_hospitality.pdf

Since none of these companies are fond of you buying direct, and you don't know a whole lot about the integration, it would be a lot simpler to use the Locate an installer tab above and make someone else do it. Yes, you'll put some bills in his pocket, but you'll also end up with
someone who understands your system and makes it work.

Just my .04 worth.

Carl