If I could not really use a computer at the moment, I would look at the biggest project dependencies, if some are unknown to me (or I don’t know them enough) I would instead spend sometimes reading their documentation.
It does not fully answer the question, but I think I would still gain valuable knowledge about the codebase indirectly, rather than being utterly slow trying to navigate a big codebase on my phone.
Call back the person you foolishly told to expect an immediate appraisal and remark 'I have investigated that old codebase.'
Set up an appointment to discuss it at length and then browse it more comfortably over the weekend on a normal screen instead of torturing your corneas
If you have exceptionally good eyesight and skinny fingers, then any browser should be fine, just like on a desktop, using the mouse only. Once the on-screen keyboard pops up it would be even more difficult.
As for myself, I need glasses and have thick fingers, so I would even think of trying.
It does not fully answer the question, but I think I would still gain valuable knowledge about the codebase indirectly, rather than being utterly slow trying to navigate a big codebase on my phone.