אחרי העדכון הזה, הגרסה החדשה עובדת מהר יותר.

Because that is the normal Hebrew pattern.

In English, we say this update.
In Hebrew, you usually say update this:

• העדכון הזה = this update
• הספר הזה = this book
• היום הזה = this day

So the word order is different from English, but completely normal in Hebrew.

Hebrew normally makes the noun definite when using this/that with it.

So:

• העדכון הזה = this update
• not standard: עדכון הזה

This is similar to what learners sometimes call double definiteness: the noun is marked as definite, and the demonstrative also appears.

Also, הזה must match the noun:

• העדכון הזה — masculine singular
• הגרסה הזאת — feminine singular

Since עדכון is masculine, הזה is the correct form here.

In Hebrew, adjectives usually come after the noun.

So:

• הגרסה החדשה = the new version
• literally: the-version the-new

This is the normal order in Hebrew:

• ספר טוב = a good book
• הספר הטוב = the good book

So הגרסה החדשה is exactly what you would expect.

Because when a noun is definite, its adjective is usually definite too.

So:

• גרסה חדשה = a new version
• הגרסה החדשה = the new version

This is an important Hebrew pattern.
If the noun has ה־ and the adjective describes that specific noun, the adjective usually gets ה־ as well.

Because the subject, גרסה, is feminine singular.

In Hebrew present tense, the verb agrees with the subject in gender and number:

• masculine singular: עובד
• feminine singular: עובדת
• masculine plural: עובדים
• feminine plural: עובדות

Since הגרסה is feminine singular, the sentence uses עובדת.

Compare:

• המחשב עובד = the computer works
• הגרסה עובדת = the version works

It can mean either, depending on context.

Hebrew present tense often covers both:

• works
• is working

So הגרסה החדשה עובדת מהר יותר could literally be understood as either the new version works faster or the new version is working faster, but in this context the natural English translation is works faster.

Hebrew often forms comparatives with יותר = more.

So:

• מהר = fast / quickly
• מהר יותר = faster / more quickly

Literally, it is something like fast more.

This is a very common Hebrew pattern:

• גדול יותר = bigger
• טוב יותר = better
• לאט יותר = more slowly

So עובדת מהר יותר = works faster.

Because here Hebrew is describing how it works, not what it is like.

• מהר is functioning as an adverb: quickly / fast
• מהירה is an adjective: fast (feminine)

So:

• הגרסה החדשה עובדת מהר יותר = The new version works faster
• הגרסה החדשה מהירה יותר = The new version is faster

Both are possible, but they are structured differently.
The sentence you were given uses the verb עובדת plus the adverb מהר.

Here אחרי means after in a time sense:

• אחרי העדכון הזה = after this update

Yes, לאחר can also mean after, and it is often a bit more formal:

• אחרי העדכון הזה — common, everyday
• לאחר העדכון הזה — a little more formal

So both are possible, but אחרי sounds very natural in ordinary speech and writing.

The comma is not always strictly necessary, but it is very natural in writing because אחרי העדכון הזה is an introductory time phrase.

The sentence structure is:

• After this update,
• the new version works faster.

Hebrew often uses a comma after an opening phrase like that, especially in careful writing. It helps separate the time setting from the main statement.