are surge protectors bi-directional?

I'm just a computer nerd, ignorant of matters electrical and networking.

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My question: are surge protectors bi-directional?

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Motivation: Denver Colorado can get vigorous thunderstorms.

Wondering if lightning side flash could flow in through coax on a cable modem,

into the modem's surge protector, and upstream into the house circuit?

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Overview: what I'm planning (details below):

1) Whole-house surge protector (type2 at panel).

2) Computer & network gear: surge protectors (maybe UPS later).

3) ethernet: Cable modem to switch isolation (fiber + media converter).

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My main question is on (3), but I'd welcome any advice you can offer on my blind spots.

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For (3) Cable modem, I'm wondering if lighting side-flash via coax something to worry about? (Comcast xfinity if it matters.)

I'll have the cable modem powered through a surge protector, which will be dowstream from the whole-house surge protector. Which got me wondering, are surge protectors bi-directional?

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I've read that coax surge protectors don't do much, and may mess with the internet signal, so I'm planning on skipping that for now (I'm open on this point; I don't know enough to have an informed opinion).

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Parts & Details:

whole-house surge protector:
I was browsing this article, seems like the Eaton CHSPT2ULTRA is a good unit.

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wall plug surge protectors:
To get started, I'm putting APC P12U2 surge protectors on computer gear (laptop chargers, desktop, monitors). Basically everything that the computers physically connect to. Maybe uninterruptible power supplies later - I still need to research that.

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ethernet:
Fiber isolation w/media converters, seems easier to get a new cable modem. For roughly $100 this seems like cheap insurance.