Can the modal auxiliary verbs be considered to be in the present tense (form, not meaning)?

According to Practical English Usage by Michael Swan, modal auxiliary

verbs do not normally have past tenses:

The modal auxiliary verbs are will, would, shall, should, can,
could, ought, may, might, and must. Their grammar is different from
that of other verbs: for example, they have no infinitives,
participles or past tenses [...] Modal verbs do not have infinitives or
participles (to may, maying, mayed do not exist), and they do not
normally have past forms.

So can each modal auxiliary verb be considered to be in the present tense
(in form, not meaning)? Since the modal auxiliary verbs are finite and they
do not have past tense forms (according to Michael Swan's Practical English
Usage), each must be in a present tense form.

Or are will, can, may and shall the present tenses (in form, not
meaning) and would, could, might and should the past tenses (in
form, not meaning)?

What about the modal auxiliary must?