The clean way is connecting Thunderbird to the account and letting it download the mail, since Hotmail, Outlook.com and Live are all the same Microsoft mail accessible to Thunderbird over IMAP with modern authentication, so the setup then the local backup step:

Connect the account with OAuth2, the modern requirement: add the account in Thunderbird with your Hotmail address, and Thunderbird autodiscovers Outlook.com's servers, imap-mail.outlook.com and smtp-mail.outlook.com, authenticating through Microsoft's own sign in page for the OAuth2 that these accounts now require, MFA included. Where autoconfig stumbles, set the servers manually with the authentication method as OAuth2. The full mailbox then syncs into Thunderbird, folders intact, over IMAP.

The important distinction, IMAP syncs rather than exports: connecting over IMAP mirrors the server in Thunderbird, so the mail shows but still lives on the server, meaning this alone is access rather than a local backup that survives the account. For actual local ownership, the next step matters.

Make a genuine local copy: create Local Folders in Thunderbird, then select the IMAP account's messages and copy or drag them into a Local Folders folder, which downloads them onto your machine independent of the server, the real backup that persists even if the online account goes away. For bulk, the ImportExportTools NG add-on exports folders to mbox or EML for an even more portable archive, the belt and braces local copy.

The full result: the account connected over IMAP for ongoing access and offline reading, plus the mail copied into Local Folders or exported via the add-on for a genuine local backup independent of Microsoft, together giving you both the live account in Thunderbird and the durable local copy the backup goal wants. The OAuth2 sign in is the piece people miss, so if connection fails, ensuring the authentication method is OAuth2 rather than a normal password resolves most setup failures.