AppleScript : searching for a tab on chrome and saving the tab as a variable
Summary (TL;DR)
Store a reference to a tab or window
Either by id (which is fixed):
    set T to the id of the current tab in the front window
    ...
    set the URL of tab id T of the front window to &quot;https://apple.stackexchange.com/&quot;

Or by object (which is fixed):
    set T to the current tab in the front window
    ...
    set the URL of T to &quot;https://apple.stackexchange.com/&quot;

BUT not by index (which changes).

You have a couple of options when storing references to objects (such as tabs) in AppleScript.  Specifically, you're asking about the id property of the tab.  You have to be mindful here: there are two ways of referencing Chrome tabs and windows using numbers:
Referencing Tabs/Windows by id/index

❶・By index: e.g. tab 2 of window 1

This refers to the ordered position of the tab from leftmost to rightmost, i.e. tab 1 refers to the left tab, tab 2 refers to tab to the right of tab 1, etc..
These indices change if tabs move, open and close.  For example, if you close the middle of three tabs, tab 3 then becomes tab 2.
With the windows collection, the index is the ordered position of the window from frontmost to rearmost, ordered by which window most recently received focus.  window 1 is synonymous with the front window, and currently has focus.  When you switch to a different Chrome window, this now becomes window 1, and the previous window 1 is now window 2.
Therefore, referencing an object and storing references to that object by its index property is a very unreliable method, with the exception of references to the front window or front tab where it only matters that the object currently has focus, regardless of which one it is.  Therefore, tell the front tab of the front window to... is perfectly reasonable use of the index, and probably the only one.
Note, that the index property is a named property for window objects, which can be read and set (set it to 1 to bring it to the front).  Although tab objects do get referred to by an index property, it is not a named property that one can read or set.

❷・By id: e.g. tab id 54 of window id 53

This is a unique, fixed property assigned to each object at the moment of its creation, and it typically ascends in value as each new object in a family of similar objects is created.  So, generally speaking, window id 2088 was created after window id 25.
Importantly, the id provides a fixed reference value with which you can reliably and safely store objects in variables for later use, knowing that they will still refer to the exact same object regardless of where in your script the variable is evaluated and how the arrangement of objects has changed (until the object is destroyed).
Setting and Getting The Variable
When you wish to assign a reference to a tab or a window to a variable, you can choose to:
either store its actual id property value, then reference the tab by its id later on, the value of which will be the value of the variable;
or you can store the entire object itself in an AppleScript variable.  This is often the easiest.
By id
To store by id, you can do so like this:
    set T to the id of the active tab of the front window

In Chrome, the active tab of the front window might return tab id 34 of window id 2045.  The id of that tab object is 34, so T gets assigned the value 34.
Then, later, to perform actions on that same tab, which may no longer be the active tab, you can do so like this:
    tell tab id T of the front window to execute JavaScript...

(assuming the front window is still window id 2045; otherwise, you'll have to store the window id value in a separate value too.)
Note that the reference is to a tab id T and not tab T, which would be tab 34 (i.e. index 34, if you had 34 tabs open).  The id label must be included.
By Object
To store the tab object itself, which is often preferable, you do so like this:
    set T to the front tab of the front window

Although I've implicitly used index values here, AppleScript actually references the tab and the window both by their id values (which it does so in almost all situations).  So if you evaluate T, you'll find it contains tab id 34 of window id 2045 and not tab 1 of window 1.
You can also assign the tab object to a variable like this:
    set T to the first tab of window id 2045 whose URL is &quot;chrome://newtab/&quot;

and T will contain tab id 30 of window id 2045, which you can later call on to perform actions within/upon:
    set the URL of T to &quot;https://stackexchange.com&quot;

or
    tell T to close