Extending the Standard Model (SM) by one additional Higgs doublet leads to the Two-Higgs Doublet Model (2HDM). A specific charge assignment of the SM fermions under the Z₂ symmetry leads to the Type-I 2HDM. A key feature of the Type-I 2HDM is that all the additional Higgs bosons can be fermiophobic, when their couplings to the SM fermions are suppressed. As a result, all the new Higgs states can be fairly light, ~ 100 GeV or less, without being in conflict with the current data from the direct Higgs boson searches and the B-physics measurements. In a recent study Ref. [1], which this proceeding is based on, we established that the new neutral as well as the charged Higgs bosons in this model can all be simultaneously observable in the multi-b final state at the HL-LHC. An experimental validation of our results would be a clear indication that the true underlying Higgs sector in nature is the Type-I 2HDM. Additionally, in this proceeding we discuss the prospects of our work in the future e⁺e⁻ colliders.