Which countries have the largest number of already proposed TWHS?
Very few countries have more than 4 such sites (8 countries):
Czechia is the leading country with 8 proposed TWHS. Following are China, India, Russia and Spain with 6 each. 5 TWHS have been proposed by Pakistan, Slovakia and Uzbekistan.
4 have been proposed by further 9 countries: Austria, Ethiopia, France, Israel, Italy, Portugal, Romania, Turkey and UK.
An interesting observation is that some of these countries are not the "usual suspects". Czechia and Slovakia have been extremely active, although with limited success compared with the intensity of putting forward proposals. Pakistan and Uzbekistan, on the other hand, have mostly had failures in this respect.

Going through the long list of pending sites made me think of African sites. As we know by now, African countries face great difficulties preparing a strong dossier for a nomination. In addition, different to the Europeans, they don't enjoy the support of stronger countries and or form a block, in which members support each other's nominations. I was, therefore, interresed in looking at what has happened and might happen in the future with pending African sites. There are sites which have been submitted, but not nominated (referred, deferred, rejected, postponed or withdrawn).

Ziwa (Zimbabwe) - a relict cultural landscape, deferred in 1999. As of 2011 some activity towards nomination can be found:
http://ghn.globalheritagefund.com/uploads/documents/document_1955.pdf

Barotse CL (Zambia) - referred in 2014. Local opposition due to development pressures led the government to halt the nomination process.
https://www.lusakatimes.com/2021/11/30/government-halts-campaign-to-have-the-barotse-plains-listed-as-a-unesco-world-heritage-site/
https://link.springer.com/chapter/10.1007/978-3-319-57165-2_14

Nyero rock painting (Uganda) - referred in 2015. I could find no information about its current aspirations.

Eastern Arc Mountains (Tanzania) - withdrawn in 2011 due to Tanzania fearing interference that would not allow to develop the region. There seems to be no progress here since 2011:
https://whs.tfcg.org
https://africanconservation.org/tanzanian-president-nullifies-application-to-grant-eastern-mountains-as-world-heritage-site-2/

Iles de la Madeleine (Senegal) - rejected in 1979, I have found no documented activity since then.

TBC

Genocide sites (Rwanda) - incomplete in 2019. Unesco recommended not to consider any sites related to recent conflicts.

Surame (Nigeria) - incomplete in 2012. As of 2013 there is documentation of the TWHS prepared for nomination:
https://bizwatchnigeria.ng/surame-on-the-way-to-become-a-world-heritage-site/

Old Oyo (Nigeria) - rejected in 1988. I have found no record of further developments.

Oke Idanre (Nigeria) - incomplete in 2010. As of 2014 there is a report on a future nomination:
https://www.thecable.ng/idanre-hills-could-become-unesco-world-heritage-centre

Lake Chad (Chad, Niger, Nigeria) - postponed for security reasons in 2021

Manden sites (Mali) - incomplete in 2019, I could find no information

Boucle de Baoulé (Mali) - deferred in 1980, 1981, 1982. In 1982 the site was recognised as a Unesco biosphere reserve.

Nyika NP (Malawi) - rejected in 1984, withdrawn in 2006

Mulanje biosphere reserve (Malawi) - deferred in 2014. In 2000 the site was recognised as a Unesco biosphere reserve.

Masai Mara (Kenya) - referred in 1997. According to the following report it should be considered for 2023:
https://www.standardmedia.co.ke/business/news/article/2001362620/masai-mara-inches-closer-to-unesco-heritage-wall-of-fame