I would like to use the same finish in my project. Unfortunately we have lost any contact with him, so I can't ask him what he used
My first thought was that your friend used conversion varnish, a two-component finish. Two-part polyurethane is an order of magnitude more durable than the toughest of 'normal' consumer-level finishes, oil-based polyurethane1, although as I mention in my Comment above I was a little wary based on how thinly the finish seemed to be applied from your description (with the grain structure still evident)2.
but given how my partner and I are using our table, I would really like to have something similar.
Conversion varnishes are not easy to apply and harder still to apply to a high standard. So although it's a good candidate for what was used it's perhaps not something worth investigating for anyone without a lot of finishing experience and limited tools.
Now that we can see a photo honestly this looks like it was finished in oil-based poly. While I can't tell you it will be durable enough to match the performance of the finish your friend used I can tell you that it's tough enough for most users on furniture in daily use, including in challenging situations like on a working kitchen table, or a dining table in a family with young children.
And the good news is that it's easy to apply to a high standard, even for the first-timer :-) The way to do this is to decant some to a fresh container, thin it down somewhat3 and apply it with rag, wad of paper towel or by brush, then wipe some or all of it off. It's this wiping away of much or all of the excess that makes wiping varnish so forgiving, since the thin layer left behind dries more reliably flat (AKA 'levels out'), attracts less dust (so less need to 'de-nib') and also dries much more quickly when the working conditions are not ideal, e.g. during colder months, in an unheated workshop or garage etc.
More on wiping varnish in this previous Answer with essentially a full description of the process from finishing guru Bob Flexner.
You want a glossy surface based on the Q which simplifies things but just to highlight this for future searchers: regardless of the eventual finish you want buy gloss anyway. A reduced-gloss result (satin/semi-gloss as well as something more matt) is easily achieved on gloss varnish, and should not normally be done with successive applications of store-bought satin or matt varnish as this tends to hide too much of the colour and feature of the wood, and at worst can look cloudy.
1 Despite the name, this type of varnish is largely something other than polyurethane. Its more technical name is uralkyd varnish, and this makes it a little clearer that it is merely alkyd varnish with some polyurethane added to improve scratch and heat resistance.
2 Normally for really top-level protection a finish (even one as durable as conversion varnish) needs to be built up enough that it would fill the grain, even of oak which has the most pronounced grain of the common furniture woods.
3 You will have to be guided by the viscosity of the varnish you buy rather than relying on a formula, as all varnishes vary somewhat depending on how much the manufacturer themselves choose to dilute their product before we buy it! But rest assured you can't over-thin, no amount of dilution will affect final hardness. So although it slows down the total finishing time (you'll need more coats) you can thin a lot, for example if you want to make the varnish as easy to apply as possible to large surfaces.
