So Roku is no longer including their purple earbuds with their audio-jack-equipped remotes, eh?
About any old earphones you have around (or purchase) with the required 3.5mm jack should work. You don't need a set with a built-in microphone, as it wouldn't be used anyway.
I don't know about this new remote, but when earphones were used with earlier remotes that had audio jacks, remote battery life took a significant hit. The earphone amp in the remote operated whenever phones were plugged into the remote, whether viewing the Roku or not, so it was best not to leave the phones plugged in when not being used.
Many find it preferable to install the official Roku app on their phone or tablet and use the app's remote listening capabilities, either via the device's speaker or attached earphones.
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T