Doubt regarding ISI M.Math

I am currently an undergrad BSc Math student (4year NEP) in a tier-3 college (admitted in 2025). I will pass out BSc in 2028 and Bsc (Honours)/Bsc (Honours) with Research in 2029. I have been preparing for TIFR, JAM, GATE, ISI M.Math and CMI Msc Entrances with self-studying at home.

As it is mentioned in eligibility criteria in ISI Prospectus as well as CMI MSc, JAM, GATE, TIFR eligibilty that for an MSc, a BSc is mandatory.

Nowhere it is mentioned that a BSc Honours is mandatory (which is 4year everywhere except ISI B.Math, B.Stat).

So my question is that will it be a good idea for me to take admission in MSc in any of these institutes after a 3-year BSc and not a 4-year BSc Honours provided I clear the exams?

This is because I am a 2024 HS Passout and took admission in 2025 for some medical reasons. My objective is to do MSc in a good institute and a Phd later in India/abroad.

Will I face any issue if I join MSc without an honours later in my career in Phd or interviews? Will there be any problem in pursuing Phd abroad after MSc if I get a chance due to my 3-Year BSc?