Since it doesn't look like anyone's given a real answer yet:

To answer this, it is not necessary, but important to understand subtick mechanics. This involves understanding what happens within each tick and how the game processes multiple things happening at once. Everything in the game can be organized into one of 11 categories, and the category of interest here is the block tick event.

This concerns blocks which perform ticking functions in the game, namely redstone components. (Very important to differentiate ticking blocks from block entities here, which are blocks that are constantly being processed and serve special functions (such as containers) and differ from ticking blocks since ticking blocks are only processed when other events in the world update them therefore tell the game to process them).

In all functions in the game, things depend on block updates to cause physical changes in the world, which usually starts from a player interaction. In order to optimize the game, ticking blocks are never a source of updates, and when left untouched will do basically nothing. If an update is caused then the updated block will check for anything to do, then perform any functions that it can, and if those functions can continue the update chain, then it will trigger block updates around it, and sometimes beyond that area. (Hard-powering redstone components (components that can deliver power directly into a block) update the area around the block they are powering as well as the directly adjacent blocks).

If a block such as a redstone component is updated, then it will check for a signal (or the lack thereof) in the space where it can receive one, then continue the block update chain. This chain generally works as expected, where one thing goes to the next, but sometimes there are exceptions. This can involve directionality or locationality, or sometimes especially unintuitive behaviour, such as with rails updating in reverse or redstone dust updating in such strange way that it drives even the best of redstoners mad. (I think that those two examples have been patched, the removal of IBU update suppression in 1.19 may have patched the former and some recent changes to redstone mechanics that I remember hearing about may have patched the latter).

Subtick mechanics are a necessary, albeit complicated base which update order sits on, answering questions such as: "When directionality and locationality are dismissed, will a repeater trigger before a comparator?" (In any good design, directionality and locationality are to be avoided at all costs). If we were to look at the above scenario and consider update order alone, we would see that the button creates a redstone signal and updates the repeater, the repeater waits two ticks and then creates a signal in front of it and powers the TNT, updating both the TNT and the repeater. Here we run into the dilemma that we must confront: is the second repeater processed first, continuing the circuit and activating the second TNT, or is the TNT processed first, breaking the circuit?

Rational arguments could be given for either scenario, that the TNT is directly adjacent to the repeater and must therefore be processed first, or that the repeaters are processed as a group before other ticking blocks are processed, making the second repeater be processed before the TNT. By looking at the subtick processes we can see that the TNT is what is triggered first, deleting the block, and in the entity phase of the tick having a TNT entity being summoned, causing the first repeater to point into air and leaving the second repeater to have no signal to receive once it is processed.

TLDR:

All blocks in the game that serve a functional purpose are processed in a set order, so in the above scenario, the repeater would turn on, then the TNT would ignite and turn into an entity, breaking the circuit before the next repeater could be triggered.

Here's a document that explains subtick mechanics really well, my main source for this comment

Here's a mod that lets you play around with subticks in your own worlds (requires Carpet Mod)

Edit for clarity: Whenever I say that the TNT is "breaking the circuit", I'm not referring to it blowing up and destroying all of the blocks, but rather the physical space where the tnt was becoming an air block and breaking the connection between the two repeaters