I would get some road or tri shoes.

MTB shoes use a different cleat than a road shoe. Its 2 bolt mounting system such as shimano spd. You are going to be limited to those type of pedals. They are slightly easier to get in and out of, so not a terrible thing for a beginner. As you progress, you'll want a 3-bolt type cleat system meant for a road style bike though. So whatever you do, I wouldn't spend a ton on this stuff as you'll likely want to upgrade.

You can get Shimano SPD mountain bike pedals (comes with the cleats) for about $40. Those will work the 2 bolt mounting system that shoe uses. You could look used, but typically if you buy used you're just buying the pedals and not the cleats. So buying new isn't a bad option here.

That said, in the long run you may want road/tri shoes that utilize a 3 bolt system for the cleats. Which means you would also need to change pedals. But that means buying shoes and pedals.

I say just buy the Shimano SPD pedals for now and use what you got to keep your costs low. They're a little easier to get in and out because they're dual sided and they are much easier to walk/run in as you're going in and out of transition for your first set of races. Once you fall in love with cycling and buy a gravel and mountain bike, you'll still be able to use them even if you switch to road/tri shoes for your road bike. :)

If I remember well, standard for cleat are different for MTB and Road/Tri (2 vs 3 attach points).

On a MTB shoe, you can only attach MTB cleat, compatible with MTB pedals.
Not sure if MTB pedals have same attachment standard than Road/Tri pedals to the crank. Never tried.

Ever you change your shoes, or you try to use low cost MTB pedals / cleats

Those are mountain biking shoes, so you will need spd mountain bike pedals. Shimano m520 pedals are the best value for money and they are bulletproof. Pedals are a wear item, so just buy them new. They are only 30 bucks anyway. There is only a small performance benefit from going to road shoes and pedals. (3 hole, wider platform, can only clip in on one side)

What about double-sided or infinite clip-in road pedals?

Another vote for getting the Shimano SBD pedals. $30-$40 bucks or so on Amazon, and make sure you get some that come with the clips for your shoes.

I'm back into triathlons after a LONG break. When I did them back in the 80's we still had cages and leather straps :) I opted for the mt bike shoes and SBD pedals. I love them. I put them on at my bike in T1, and then can run to the mount line. Then I can run from the dismount line to T2 no problem. I quickly found out that the small local tris are anything but the nice astroturf conditions, of some of the bigger IM type races. We are running through sand and gravel and grass and dirt and very rough pavement. Some of the barefoot flying mount/dismount FOP cool kids are willing to put up with that... but I'm an old age grouper, and don't do that running mount stuff anyways. At first I was thinking I would eventually go to the tri racing shoes... but after winning my age group at all the local tris, I'm happy and comfy with my mt bike shoes, and don't plan to change anything.

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Athlinks / Strava

SPD pedals with mountain bike shoes are the perfect system for someone new to clip ins in my opinion. If you got free shoes, more power to you. The performance difference between these shoes and a road shoe/pedal system is marginal.

They make pedals that are clip in one one side and have platform pedals on the other side, something like this: https://www.bike-discount.de/...gEAQYAiABEgIC6PD_BwE

With these you can ride your bike in your tennis shoes un-clipped or with your new bike shoes clipped in. Someday you may want to upgrade to a road shoe/pedal system, but these will work for a long time until you are ready to make that investment. On the flip side, it is nice to be able to ride your bike with regular shoes if you are not fully committed to a clip in system or if you wanna use your bike for commuting.