Worn-Out Routine

This title has a double meaning. In addition to the one you intend, it could also mean that the routine is worn out. In fact, that is the meaning I immediately thought of when I read it. For this reason, I would change it.

Today, I am totally worn out and I'd like to share the evening routine I stick to in such cases.

Because your writing is so advanced, you are getting feedback on word choice as relates to style. I think it's good for writers to experiment with different styles because it develops useful skills and can be fun. On the other hand, I think it is important for a piece of writing to be stylistically consistent. In this piece, "stick to it" is quite casual and informal, whereas "peruse" is the opposite. Perhaps an analogy would be composing a piece of music.

Firstly, I turn off my phone.

So the difference here is that "firstly" goes with "peruse," and "first" goes with "stick to it."

My beverage of choice is warm milk with honey, by the way.

Here you are mixing styles in one sentence: the first part is formal, yet "by the way" is very informal.
Are you starting to see the contrast?

This little habit is a great way to finish yourmy / the day!

You could make the argument that using "your" invites the reader to make a connection with you as you end the piece, and it echoes your beginning where you write, "I'd like to share."

However, the piece isn't oriented toward the reader the way an advice column might be; its purpose is to inform, not persuade, which is why I like "the" or "my."

If, on the other hand, you intended the "your day" to be generic, not personal, then we have circled back to the issue of stylistic consistency. "Your day" fits better with an informal style, and "one's day" fits better with a formal style.

Today, I am totally worn out and. I'd like to share themy evening routine I stick to infor such casedays.

Firstly, I turn off my phone.

It's full of distractions one is especiallythat one would be susceptible to under such circumstances.

It can be a family member, language exchange partner, or an acquaintance on Discord.

It's full of distractions one isI'm especially susceptible to under such circumstances.

This sentence is grammatically correct but sounds a little old fashioned.

Approximately two hours before bedtime, I take a scalding shower or bath and then peruseread something on my e-reader.

"peruse" also sounds a little old fashioned.

Today, I am totally worn out and, so I'd like to share the evening routine I stick to in such cases.

More natural to express causation

Firslyt, I turn off my phone.

It's full of distractions one is especially susceptible to under such circumstances.

Grammatically fine, but a little awkward. Another way to say this might be:
"It's full of distractions, especially when you're already exhausted."

Then, I make myself a hot drink and talk to, with my beverage of choice being warm milk with honey. As I'm enjoying my drink, I chat with someone.

Better to combine the sentences that are related to each other. Also, "chat" sounds more casual than "talk."

ItThis can be a family member, a language exchange partner, or an acquaintance on Discord.

More connected to the previous sentence

My beverage of choice is warm milk with honey, by the way.

See above

Approximately two hours before bedtime, I take a scalding hot shower or bath and, then perusefind something to read on my e-reader.

I don't usually hear "scalding" on its own. Similarly, I don't hear "peruse" that often. (Might be a dialect thing?)

OBut every once in a while, I might watch a movie with my family instead.

More of a style thing, feels more connected to the previous sentence

Before going to bed, I always clear my head by makwriting a smallhort diary entry.

Not wrong, but "writing" and "short" feels more appropriate when talking about a diary.