What is the significance of the Gita’s reference to Krishna as Bhagavan because Mahabharata also refers to Shiva as Bhagavan?

If one goes for the technical definition of the word bhagavan ,then it is given in vishnu-purana (6.5.72-75,79) as follows :

shuddhe maha-vibhuty-akhye

para-brahmani shabdate

maitreya bhagavac-chabdah

sarva-karana-karane

“O Maitreya, the word bhagavan may be defined as a name of the Supreme Brahman, who is pure, free from all material contamination, full of unlimited powers and opulences, and the original cause of all causes.”

sambharteti tatha bharta

bha-karartho dvayanvitah

neta gamayita srashta

ga-kararthas tatha mune

“O sage, in the word bhagavan, the syllable bha stands for the word bharta, which means the maintainer of everything, or the shelter upon whom everything rests, and the syllable ga stands for gamayita, the leader of everyone, or the creator and annihilator of the entire cosmic manifestation.”

aishvaryasya samagrasya

viryasya yashasah shriyah

jnana-vairagyayosh capi

sanëam bhaga itingana

“The name bhagavan stands for that Supreme Person who is full in the six opulences (bhaga) of all wealth, strength, fame, beauty, knowledge and renunciation.”*

vasanti tatra bhutani

bhutatmany akhilatmani

sa ca bhuteshv ashesheshu

va-kararthas tato ‘vyayah

“In the word bhagavan, the syllable va stands for the verb vas (to reside), because He is the Supreme Personality of Godhead in whom the entire creation rests, and also because He is the Supersoul, who remains in the hearts of all conditioned souls. The syllable va also stands for the word avyaya (unchanging), which indicates that the Supreme Person is eternally the same.”

jnana-shakti-balaishvarya-

virya-tejamsy asheshatah

bhagavac-chabda-vacyani

vina heyair guëadibhih

“In this way the name bhagavan means that person who posesses all strength, knowledge, beauty, fame, wealth and renunciation, and all other auspicious qualities, and is also completely free from any fault or defect.”

Thus in a correct technical sense ,the word bhagavan( as can be seen from the above definition ) applies perfectly to the original form of Lord Krishna .

But all those avatars of lord krishna including lila avatara ,purusha avatara ,guna avatar ,saktyavesha avatara and other types ,scriptures also refer to them as bhagavan .

Scriptures at times also refer to Avesha incarnations like Narada ,Vyasa ,Parashurama and four Kumaras also as Bhagavan .And as far as Lord Shiva is concerned ,he is considered to be the Guna Avatara of Krishna .Thus Visnu tattva expansions and anyone who is especially empowered or endowed with some specific potency of Lord Krishna ,scriptures call them as Bhagavan .

Thus Lord Shiva , have many of the qualities of Lord Krishna in common ,so , scriptures refer to him also as bhagavan ,

But in a strict and pure technical sense ,Lord Krishna is the reservoir of all the 6 opulence in full ,thus scriptures in order to distinguish Krishna from all other incarnations of Lord including Visnu ,call him ” SVAYAM BHAGAVAN ” .this usage of svayam is explicitly used for Lord Krishna only ,and not to anyone .

And thus many scriptures like Brahma vaivarta purana and Garga samhita specifically call him Svayam Bhagavan ,thus avoiding confusion .for eg

sri-sridamovaca

paripurnatamah sakshac
chri-krishno bhagavan svayam
asankhya-brahmanda-patir
golokeso virajate

Sri Sridama said: Sri Krishna is the original Supreme Personality of Godhead. He is the master of countless universes. He is the master of Goloka. ( garga samhita )

and “krsna tu bhagavan svayam ” (bhagavatam )