Can Windows 10 see ext3?

I'm in the middle of restructuring my MoCA 2.0 network. For the sake of this post, I will only list partial list of my setup for two of the three rooms

Room 1:
ONT> (Coax) G1100 Router> (Ethernet LAN to LAN) RT-AC87U>Seagate Backup Plus External Hard Drive (USB 3.0)

Room 2:
ONT> (Coax) Actiontec Access Point > Hub (LAN to Ethernet port) > Chromecast with Google TV (USB Type-C)

Basically with any connected device on my network, whether if it's a Windows 10 PC, my Chromecast with Google TV, or an iPad, I want to be able to access the files (to include backup files, audio/video files for streaming throughout the house. These files will be on the aforementioned Seagate drive.

One problem that I found, was that not only does my router only currently support NTFS, FAT and HFS, but my Chromecast will only work with ext3, for larger files, which is what I would need. For the sake of the argument, I'm going to assume that cooked router firmware will allow me to format using other file formats.

That said: Will a Windows 10 PC be able to access the drive if I format it to ext3 or do I need to install an addon to make this work?

You need additional software for this.
Often used and reliable:

How to Access Linux Ext2 or Ext3 on Windows| DiskInternals

syntoh

Via the network, I had no difficulty to access files on an ext4 formatted HDD connected to a Linux based mediaplayer (Rasp Pi).
How that works with your router I cannot predict, but probably its firmware is also Linux based