chore(analysis/normed_space/basic): `continuous_at.norm` etc (#5411)
Add variants of the lemma that the norm is continuous. Also rewrite a few proofs, and rename three lemmas:
* `lim_norm` -> `tendsto_norm_sub_self`
* `lim_norm_zero` -> `tendsto_norm_zero`
* `lim_norm_zero'` -> `tendsto_norm_zero'`
Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>