Today is Christmas Eve;. Today is Christmas Eve.

Today is Christmas Eve;. Today is Christmas Eve.

However, I started my day at Starbucks just aslike I did yesterday. However, I started my day at Starbucks just like I did yesterday.

Either "as" or "like" work here, but to me, I think "like" works better in this sentence. "...as I did yesterday" sounds slightly more... formal? It's a little hard to explain.

However, I started my day at Starbucks just as like (I did) yesterday. I started my day at Starbucks like (I did) yesterday.

Hhowever, I started my day at Starbucks just as I did yesterday. however, I started my day at Starbucks just as I did yesterday.

A semicolon is not followed by a capital letter because it functions like a conjunction (and, but, etc.) within a sentence.

Today's drinkMy drink for today was a cafe latte. My drink for today was a cafe latte.

I read the text sofquietly to myself since I was in the cafe. I read the text quietly to myself since I was in the cafe.

"Softly" can mean quietly, but in that case, I think it has a sort of romantic quality, which doesn't feel quite right in this sentence.

Arboundt two hours later, I felt sleepy, so I pulled out my iPad to doodle, hoping to stay awake. About two hours later, I felt sleepy, so I pulled out my iPad to doodle, hoping to stay awake.

But when I realized the time, it was already 1 hour pastan hour had already passed! But when I realized the time, an hour had already passed!

I'm not entirely sure if this is what you meant.

But when I realized the time, it wan hour has already 1 hour past!passed. But when I realized the time, an hour has already passed.

But when I realized the time, it was already 1 hour pastlooked at the time, an hour had passed! But when I looked at the time, an hour had passed!

If you want to use the word "realize" this might work: "when I realized what time it was, I was surprised an hour had passed."

But when I realized the time, it was already 1 hour pastan hour had already passed! But when I realized the time, an hour had already passed!

Thankfully, I felt much less sleepy thanks to doodling. I felt less sleepy thanks to doodling.

Thankfully is kinda redundant.

The cafe started to get crowded pastafter 9 a.m., so I closed the book when I reached Unit 70. The cafe started to get crowded after 9 a.m., so I closed the book when I reached Unit 70.

"past" with time is used when reporting the time (ex. half past nine). Although it means "after," its use is restricted. I say this as a speaker of American English. "Past" might sound right to speakers of British English.

I felt (?) under the weather today, so I couldn't study as much as I expecthad hoped. I felt (?) under the weather today, so I couldn't study as much as I had hoped.

You felt like you were below the weather? The first part of this sentence is a little bit strange. It feels like there should be an adjective where the (?) is.

I felt under the weather today, so I couldn't study as much as I expected. I felt under the weather today, so I couldn't study as much as I expected.

This idiom is fine just as it is. (A simple Google search will show it even in dictionary entries.) Also, there is nothing wrong with using "expected" here.

I'm going to take it easy tomorrow to recharge, so I can have a better day the day after tomorrow. I'm going to take it easy tomorrow to recharge so I can have a better day the day after tomorrow.