What is Trezor Suite actually doing?

I just got a Trezor T, and I've got some questions.

Up to this point, I've used different software wallets to store the various coins I have. Let's use BTC, ETH, and ADA as examples.

When I created a Bitcoin wallet, I wrote down a seed phrase.

When I created an Ethereum wallet, I wrote down a seed phrase.

When I created a Cardano wallet, I wrote down a seed phrase.

I can wrap my head around this: different blockchains, different private keys.

When I was setting up my Trezor T via Trezor Suite, I had to write down ONE seed phrase (not a single word, but a single list of words).

But then I noticed that in Trezor Suite, I can manage multiple coins, the three above included.

How come I have a single seed phrase for all these coins on different chains?

Also, I'm not sure I understand what Trezor Suite is. Is it a wallet? Moreover, I've noticed there are other software wallets that have Trezor support (Electrum for BTC, MEW for ETH, Daedalus for ADA). If that's the case, why would I use Trezor Suite?

What is Trezor Suite actually doing?