None of them is posh anymore. Oscar was an UMC name until about 15/20 years ago when it rocketed in popularity.
George and Henry are classic boys’ names which have been, and still are, used by the upper classes, but 100 years ago there were lots of working class Georges and Henrys, and they have similarly had a resurgence in the past 15 years. I’d say Leo and Max are similar but have not been as popular historically as George and Henry.
In general, the true ‘upper classes’ use a fairly small pool of boys’ names, which at times will also be popular more broadly and at others, won’t. The upper middle classes and upwardly mobile/aspiring upper middle classes use the more elaborate names (Horatio, Tarquin, Ptolemy); not to say that you won’t ever find an aristocratic Atticus, but these names are less ‘posh’ than the people who choose them think.
A good example: Princess Diana wanted to call William either Oliver or Sebastian (very Sloaney names in the early 80s) but had to settle for something more appropriately aristocratic.
All of which is a very long-winded way of saying that there’s considerable overlap in the names that posh people and middle or working class people use in one respect: the well-established Biblical or royal names.
Modern or faddy names (Jayden, Kai etc) are usually working class.
Latinate or Ancient Greek-derived names (Tarquin, Peregrine etc) are usually aspirational middle class.
James could be a King or a carpenter.