There's no solid definition of "boat" versus "ship", but those are clearly a different scale.

Water depth in the Rove tunnel is 4m, and 12m in the Stad tunnel. They don't say at what state of the tide that is though, which I would have thought affects the size of ship that can pass through significantly (unless it has locks either end I suppose).

From Wikipedia:

Rove:

    Length - 7,120 metres (23,360 ft) long
    Clearance - 15 m (49 ft)
    Width - 22 m (72 ft)

    Length - 1800 metres
    Clearance - 49 metres
    Width - 37 metres
    Boat-passable - 16 metres
    Depth of tunnel below water level - 12 metres

And do not forget the various military ship tunnels out there.

https://en.wikipedia.org/wiki/Naval_museum_complex_Balaklava

https://www.cnn.com/2020/08/21/asia/china-submarine-undergro...

There isn't a single, fixed definition of "ship". From https://en.wikipedia.org/wiki/Glossary_of_nautical_terms_(M%... , "2, More generally, any medium or larger seagoing vessel. Smaller vessels or those used in sheltered waters are generally called boats. Exceptions include submarines, which are always referred to as boats." (See also https://en.wikipedia.org/wiki/Ship#Nomenclature ).

The Rove Tunnel was designed for canal boats and barges, not ships. From a 1928 article:

"Barges are built for quiet waters, so their masters have looked with alarm at the prospect of taking them through the Mediterranean waves 25 miles from Marseille to the mouth of the Rhone. The new canal, after permitting barges to pass through the mountain, admits them to the Etang de Berre and thence to a canal which joins the Rhone at the famous old Roman town of Arles, 49 miles to the north" - https://archive.org/details/sim_national-geographic-school-b...

The desire for sheltered waters means these vessels were boats, not ships.

Looking through old articles and you'll see descriptions like "The 4½-mile Rove Tunnel floats barges and small boats" (https://archive.org/details/sim_national-geographic-school-b...) and " this tunnel will allow passage of river boats that previously found it practically impossible to negotiate the 30-mile sea trip from the mouth of the Rhone to Marseilles." (https://archive.org/details/sim_scientific-american_1928-01_...) but I found no mention of ships using the canal.

That said, "If you own a vessel in the UK that you intend to go to sea with" and the boat is "less than 24 metres in length overall" then you can register it in the UK Small Ship's Register (https://ukshipregister.co.uk/registration/small-ships-regist...), which technically means that something described as a "ship" could have gone through the canal.

But that's not really what people generally mean by ship.