Say it’s mobile happens at least on the tablet, as some variations (mainly visual) are noted.
Might be something WP is doing rather than Chrome? Think it’s been that way for years. No problem with others e.g. MS Answers.
Edit: As it turns out, the “Keep Me Signed In” option is not set as default. Fair enough, guess the menu login item wants a facelift. 😜
Edit2: Funny, on the old mobile “Remember Me” was there – go fig.