Excel opened your CSV, decided 02134 was the number 2134, and saved it that way. Drop the file here, pick the columns, say how long the values should be, and get them back — plus an export Excel won't strip again. Nothing leaves your browser.
Tick the columns that should have leading zeros. Columns that look numeric and short are pre-ticked as a guess — check them.
5 for US ZIP, 3 for area codes; Canadian postal codes aren't numeric, so they're not affected.
A CSV is plain text; it has no idea of "text column" or "number column". When Excel opens one, it guesses, and anything that looks like a number becomes a number — so 02134 becomes 2134, 0012 becomes 12, and a phone number becomes a very large integer. The zeros were never "in" the file after the first save.
Two ways to open a CSV without losing them:
="02134", which Excel reads as text. It's a well-known trick and works in every version. Google Sheets and LibreOffice read it too.If the values are mixed — some 4 digits, some 5 — the "pad to length" setting assumes they should all be the same length. If that isn't true for your data, fix the sources instead of the symptoms.