What do the names of the days of the week in Spanish mean?

Not really. While “Shabbat” is similar to the Hebrew word for seven, “Sheva”, it actually comes from the Semitic root S-B-T, which means “to halt”, “to rest” or “to be quiet”.

To elaborate:

Sábado, Domingo, Segunda-feira, Terça-feira, Quarta-feira, Quinta-feira, Sexta-feira

Saturday and Sunday, as mentioned, mirror Spanish.

Monday through Friday have the word feira in their names, which means market, such as a farmer’s market. This means the days are really “second-market”, through “sixth-market”

Brazilians often will clip off the “feira” part in conversation. “Na segunda eu tenho que voltar para trabalho.” (I have to go back to work on Monday)

Hmmm… I wonder if there’s a link!
We say Sixth Market, you say Sixth Day. Maybe the Portuguese term wandered from its origin a bit? Regardless, a Brazilian hearing “Sixth” will think “Friday”, as will, I suspect, a speaker of Hebrew.

Irish:
Monday = Dé Luain (from Latin dies lunae Moon Day)
Tuesday = Dé Máirt (from Latin dies martis Mars Day)
Wednesday = Dé Céadaoin = first fast day
Thursday = Déardaoin = day between the two fasts
Friday = Dé hAoine = fast day
Saturday = Dé Sathairn (from Latin dies saturni Saturn Day)
Sunday = Dé Domhnaigh (from Latin dies dominicus Lord’s Day)

From the above you might conclude that the Irish word for “day” is “Dé”. You would be wrong!

To add a layer to this explanation, the surface meaning of the words is:
Sunday/nichiyobi (日曜日=太陽/←”taiyo”/”sun”) - SUN DAY
Monday/getsuyobi (月曜日=月/←”tsuki”/“moon”) - MOON DAY
Tuesday/kayobi(火曜日=火星/←”kasei”/”mars”) - FIRE DAY
Wednesday/suiyobi (水曜日=水星/←”suisei”/“mercury”) - WATER DAY
Thursday/mokuyobi(木曜日=木星/←”mokusei”/jupiter”) - WOOD DAY
Friday/kinyobi (金曜日=金星/←”kinsei”/“venus”) - GOLD DAY
Saturday/doyobi (土曜日=土星/←”dosei”/“saturn”) - EARTH DAY (earth the substance/element, not Earth the planet)

The connection with the names of Roman gods is therefore at one remove.