Using New Outlook on Windows for personal email, calendar, and contact management
I believe the answer is that you don't in New Outlook. It's not a feature available for consumer users. You have to pay for a business plan with your own custom domain so that you can create a shared mailbox and delegate that shared mailbox to the people that you want to have the contacts. This works with both mobile Outlook app by adding a new account and selecting add shared mailbox under Microsoft 365 option and for Outlook on the web, you have to access the contacts by going to the circle with your initials in the top right corner and select Open Other Mailbox and a new tab will open once you put in the "other person's" mailbox which includes a separate people section. There isn't a way to see it directly in your mailbox in a browser/Outlook on the Web (OWA).
If you do need the contacts in your mailbox, then you could use a third-party synchronization product like SyncGene or CiraSync. They have free tiers but they're limited and have to pay for more access if you have over 500-1000 contacts, etc. Again, this requires upgrading to the Microsoft 365 plan that allows this kind of connectivity administration.
As someone else mentioned, there's also just paying for a Google account using third-party plugins like Contact Sharing for Gmail but again, those are paid products on top of Google paid accounts.
It seems like this a paid functionality. We're so used to getting stuff for free in exchange for being the "product" for advertisers. The party's over? The long-term harm that the algorithm is doing on society and our children is starting to be understood?