I do not hear a difference in recordings. However, note that in the case of Psalms 1, אַ֥שְֽׁרֵי has a shewa gaʿya and is therefore naʿ. In fact, massorah holds that it should be pronounced as a full vowel.
"The Karaite transcriptions into Arabic indicate that shewa gaʿya was
pronounced as a long vowel, since they represent it with a mater
lectionis, e.g., باناحلا בְֽאנַאחְלָ֔א (בְּֽנַחֲלָ֔ה bə́-naḥălå̄́ ‘as
an inheritance’ Josh. 13.6, BL Or. 2547), كاموخام כְֽאמוֹכֶ֗אם
(כְּֽמוֹכֶ֗ם kə́mōḵέm ‘as you’ Job 12.3, BL Or. 2552), عاطيشوثاو
עְַֽאטִישׁוֹתָאו (עְַֽטִישֹׁתָיו ʿăṭīšōṯå̄́w ‘his sneezings’ Job 41.10,
BL Or. 2552)." (Gaʿya, G. Khan, Encyclopedia of Hebrew Language and
In Psalms 2 this is not the case: אַ֝שְׁרֵ֗י.
See also https://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0013_0_13385.html