Hot water and underfloor heat

Well let's see here. You refer to a gas hot water tank. Do I presume that you are referring to a gas hot water heater? Or are you referring to a gas fired boiler? If so, what are you using for domestic hot water?

What heats the rest of the house (you refer to the "main furnace thermostat")?

How is the downstairs heat piped? From the hot water tank around (circulator pump?) and back to the tank? Is that pump what controls the circulator? What turns the gas on in the "gas hot water tank"?

And last -- how does your domestic hot water fit in to this?

There are several possibilities... the thing which concerns me about it is that it sounds as though the underfloor heating may not be separated from the domestic hot water. Honestly, that is not good practice, as there are a variety of dismaying bacteria which can grow in the nice warm underfloor heating pipes -- and get back into the domestic hot water, where you really don't want them.

You probably do need to have a plumber -- or better, a person well qualified in heating -- come and look at the arrangement and, most likely, suggest changes which will give you better heat, better hot water, and better safety. Have you checked the "find a contractor" tab above for someone near you? Or if you tell us where you are, we may know someone who serves your area.

Just spitballing at the info provided, but I am going to guess that the radiant underfloor and domestic are both fed from the same water heater as an open system. Even if it is separated with an exchanger (which it should be), if the radiant draws more BTU than the water heater can recover from, there will be little or no heat left to use for domestic water after the radiant has been running for awhile and it needs time to recover. Pictures will hopefully tell the story

It looks like an open system, I certainly don't see a heat exchanger. It looks like this water heater was originally designed for use with an air handlers. I don't like it. I'd make sure that circulator is bronze or stainless steel. I'd consider getting a plate heat exchanger and changing the pipe on the T&P to copper. PEX isn't supposed to be used for that. You may be running out of water due to poor sizing of the system, or excessive build up of scale.
Get a boiler and maybe use the tank as a buffer tank.

I believe that is a legal system in Canada, a combined radiant/ DHW, you do have a stainless circulator. The Apollo is a listed tank for combined systems. I think the Canadian code requires the circulator run every 24 hours for a period of time to prevent extended stagnation.

I feel more comfortable with a separate system, either use that tank and isolate with a plate HX, or consider a Combi boiler or the boiler specific options.

A heat load calculation should be the first step, followed by a design indicating operating temperatures required, etc.