If you check the examples at the link I gave you can see that those are all very small !! Largest I believe was only 15 inches tall !! Today we have jewelry chests that are larger than them !!
Are you planning to sell this chest ?? If so,, I would leave it as-is !! Buyers of this sort of chest want them original !! Repairs or restorations,, unless you really know how,, can reduce any value by 50 to 80% !! And remember,, I can only date this chest by what I can see,, it could be older than my estimate !!

I would even think about the apothecary chest as it is quite small but when you mentioned herbs then I can imagine that would fit ,
it is not in a very good condition so I will try to fix it
thank you very much for that

https://www.antique-bottles.info/medicine-chests/

I think what you have is an antique apothecary chest !! Look above the bottles at the link above and scroll down to see several variations !! I am not sure that the symbols were original to the chest except for the leaves at the top
and sides !! By it having the leaves I would think it may have been as herbalists chest !! Cant see the symbols well enough to tell !! Its possibly from the turn of the century, 1900 to about 1930 just from what I can see !! Value would depend on its condition !!
These came in many configurations depending on what the user needed !! Some had places for medicine bottles and others did not !!

Is that a W in the triangle ?? Does it say anything else ?? Or any symbols there ?? Are you in the UK ??