Connecting flight in Tel Aviv

Timatic (the database used by airlines to determine eligibility and required documentation -- note that I randomly picked UK citizenship, you may want to "change search" to get results for your actual citizenship) currently states:

Admission and Transit Restrictions:

Passengers are not allowed to enter and transit.

Information: This does not apply to passengers with an authorization letter issued by the Population and Immigration Authority.

Information: This does not apply to passengers with an A1 or A5 visa issued by Israel.

Information: This does not apply to passengers with an A2, A3, A4, B1, B3 or B4 visa issued by Israel, if they are not arriving from Argentina, Belarus, Brazil, Cyprus, Georgia, India, Kyrgyzstan, Mexico, Russian Fed., South Africa, Spain, Turkey, United Kingdom or Uzbekistan.

(emphasis mine)

Since you're arriving from Cyprus, the last case does not apply to you, so the only way you could enter or transit would be to have "an authorization letter issued by the Population and Immigration Authority" or "an A1 or A5 visa issued by Israel".

Note that even though you have no checked baggage:

• Since your two flight are booked separately, for Ryanair your final destination is Tel Aviv, so you need documentation to enter Israel, not just transit airside;

• For at least El Al flights departing from TLV you need to be present at the check-in desk at least one hour before departure, even if you check-in online (which these days is anyway often impossible), so again, you'll need to enter Israel.

It doesn't really change things in your case anyway since the prohibition is the same for entry and transit into Israel.

Note that even if you had a permit, you would need to undergo mandatory quarantine for 24 hours or until a negative test result, and leaving Israel before the end of the quarantine is not allowed.

Note that changes are planned for 14 September (Cyprus moves from orange to yellow list), 19 September (entry allowed for groups of 5 or more fully vaccinated), October (group tours for individual travelers) but as far as I can see no changes are planned for transit yet.

Also note that in addition to COVID-related restrictions, you may need a visa to enter Israel even for transit (TWOV doesn't apply here), depending on your citizenship.

Just regarding transit, since it is a different PNR, you have to call the checking gate and pray that they will send someone to open the connections door, they really do not like, in Sep 2018, according to this, 142 did a connection in TLV! More into here: https://flying-out.com/2018/10/23/tlv-connection/