There are TWO ways of using email. The first is the 'proper' way (i.e. the system that email was designed around), using a dedicated email client. ('Client', in that sense, is just another word for 'program' or 'app'). Examples of email clients are Outlook (the software, not the website), Outlook Express, Thunderbird and the Windows 10 Mail app
The other is to use webmail, where you use your computer's web browser (such as Internet Explorer, Edge, Chrome, Firefox, Safari, Opera or whatever) to visit the website of your email provider and send your mail from there.
I suspect that you're using webmail to send your Gmail and TalkTalk emails. If so, you can use either of those services to send a Word document by first saving the document, then going to the relevant email website, creating a new email and attaching your Word file to it.
However the 'Send to' (or 'Send') function within Windows programs can't use webmail. It relies upon being able to open an email client and then attaching the relevant file to a blank email.
On your old laptop you probably had Outlook Express (or possibly something similar) set up as your default email client (
with your account settings configured within it) . When you clicked on 'Send to', that software was launched so that you could send your document off.
With your new laptop (unless you've made any changes) it will be the Windows 10 Mail app that gets launched when you click on 'Send'. However if you've not given that app the information it needs about your email account, there's no way that it can actually send an email.
So I suspect that you've not yet told the Windows 10 Mail app which email account you want to use in order for the 'Send' feature to work. i.e. have you followed the instructions here?
https://support.office.com/en-gb/article/set-up-email-in-the-mail-app-for-windows-10-7ff79e8b-439b-4b47-8ff9-3f9a33166c60