तनुँ = चंद्र बिंदी
that pull inside/surface/outside
that pull push चंद्र बिंदी is considered ण (refers to whetting)
float pull push
float pull inside/surface/outside
bamboo (as float) pull push
Tumbi verb(pull) inside

धातु अर्थ
विस्तार = वि + स्तृ + घञ् = objectify (alternate spread) = objectify(shedding)
at श्रद्धोपकरण = श्रद्धा + उप + करण
wish to hold tumbi upright in water (by) doing rope stone water push
instrument of/from (collection of (way of Erect Superior + held/carried)) =
instrument of (long superior/flow carried)

रूढ अर्थ

  1. spread
  2. thinning

Commentary
तनु originally meant pulling tumbi inside water. This is “shortening” and hence it also got to mean “to shorten”

It is possible that श्रद्धा meant something on these lines -
When तनुँ was added as an entry in धातु पाठ, it was already a relic “instrument of/from (collection of (way of Erect Superior + held/carried))”
There are only two words explained using the word “श्रद्धा” in धातु पाठ. Another is चन्.