Many sources claim that the Sun is around $70-74\%$ hydrogen and $25-27\%$ helium by mass, or $91\%$ and $9\%$ by atom count, without any further caveats - e.g. 1, 2, 3. I believe these sources are incorrect. (Especially bad ones will report photospheric atom ratios as mass ratios, like space.com here.)
More careful sources like this (from which I think many of the less-good sources above derive) or Wikipedia (citing this page) give the same numbers, but clarify that they only measure the composition in the photosphere, where we can analyze the spectral lines. I'm curious about the overall distribution across all radii (which ought to have more helium, since it's produced in the core and my impression is that there isn't a ton of mixing between layers - sources like this paper seem to suggest that would be true, but don't mention concrete numbers).
This helpful answer linked to some informative plots of the distribution by radius from this paper, which mostly answers my question, but the paper doesn't actually provide the relevant integrals of their plots weighted by radial density - just going off of the fact that the core contains around $34\%$ of the mass within $0.2$ solar radii and eyeballing the plot, it looks to me like the overall composition is something like $65\%$ hydrogen and $35\%$ helium, but if someone has worked out the actual numbers from our current best models I'd love to see those instead.