"C’est" and "est" are not interchangeable.
"C’est" is a contraction of "ce est" (which you would never say, by the way). Its literal translation is "it is." It has both a subject and a verb.

C’est la ville parfaite pour elle.
It is the perfect city for her.

"Le truc c’est qu’il n’aime pas travailler" should, strictly speaking, have a comma, like so: "Le truc, c’est qu’il n’aime pas travailler." "C’ " is the subject of "est," not "le truc."
Same goes for "L’autre chose qu’il aime c’est faire la fête." It should be "L’autre chose qu’il aime, c’est faire la fête." If you were to translate it literally to English, it would sound really awkward, like "The other thing he likes, it’s partying."

So, if you change the subject of the sentence to be "le truc" or "l’autre chose qu’il aime faire," you can use "est" instead of "c’est" ("Le truc est qu’il n’aime pas travailler", "L’autre chose qu’il aime est faire la fête"). But there needs to be a subject for the verb, which is why you couldn’t do that for "C’est la ville parfaite pour elle." You would have to reword it to "La ville est parfaite pour elle."

Finally, you are correct, using "c’est" is less formal than using the subject directly with its verb.

I hope this helps!

”C’est” is what we call a présentatif in French grammar. Why? Because it grammatically introduces présente more often than not something or someone.

The French phrases ”c’est” and ”il/elle est” can be tricky because they are close grammatically but not interchangeable. * Which one to use depends less on meaning than it does on grammar.

For example…

J’aime ce tableau. Il est joli. I like this picture, it’s pretty.
C’est un joli tableau. It’s a pretty picture.

Another important thing to remember is that "c’est" is neuter, which means it takes the masculine for by default. Assuming you’re referring to something feminine but you decide to use it to convey generality.

I.g. Wow, c’est beau ! – Wow, it’s beautiful! What is beautiful? Could be the river (which is feminine in FR), could be the lake (which is masculine in FR), but it isn’t specified, so we use "c’" and therefore keeps its default masculine form.

If we modify the the action by a different verb, this can also happen, these context are colloquial however:

EX.

–As-tu rangé ta chambre ? (Did you clean your room?)

-Oui, maman, c’est fait ! (Yes, mom, it’s done!)

Here we’re not using the same verb, therefore the subject is elided, and can be replaced by "c’" instead of the more proper way keeping the action verb intact.

EX.

–As-tu rangé ta chambre ? (Did you clean your room?)

-Oui, maman, elle est rangé/je l’ai rangéE (Yes, mom, it is cleaned/I cleaned it)

Common trick for some cases: if it’s followed by a determiner it’s usually "c’est" if it’s followed by an adjective, more often than not, it’s "il/elle est"

C’est + determiner + noun (with or without an adjective)

C’est le docteur. That’s the doctor.
C’est ma jeune sœur. She’s my younger sister.
Ce sont nos voisins. Those are our neighbors.
Ce sont des amis intimes. They’re close friends.

Il est + adjective:

Il est sympa. He’s nice.
Elle est intelligente. She’s smart.
Ils sont sages. They are wise.
Elles sont belles. They are beautiful.

Here’s a good website on the difference to further your understanding, if needed: https://www.lawlessfrench.com/grammar/cest-vs-il-est/