Ecclesia and its derivatives does always carry a connection with the Church, and has done since the word was used in the Gospels and the writings of St Paul.
κἀγὼ δέ σοι λέγω ὅτι σὺ εἶ Πέτρος, καὶ ἐπὶ ταύτῃ τῇ πέτρᾳ οἰκοδομήσω μου τὴν ἐκκλησίαν, καὶ πύλαι ἅδου οὐ κατισχύσουσιν αὐτῆς.
I also say to you that you are Peter, and upon this rock I will build my Church; and the gates of Hades will not overpower it. (Mt 16:18 NASB)
τῇ ἐκκλησίᾳ τοῦ θεοῦ τῇ οὔσῃ ἐν Κορίνθῳ, ἡγιασμένοις ἐν Χριστῷ Ἰησοῦ, κλητοῖς ἁγίοις, σὺν πᾶσιν τοῖς ἐπικαλουμένοις τὸ ὄνομα τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ἐν παντὶ τόπῳ, αὐτῶν καὶ ἡμῶν:
To the church of God which is at Corinth, to those who have been sanctified in Christ Jesus, saints by calling, with all who in every place call on the name of our Lord Jesus Christ, their Lord and ours: (1 Cor 1:2 NASB)
To my knowledge the word has not been claimed by or applied to other religions.
A suitable alternative might be religiosity, or your own theism.
religiosity: Strong religious feeling or belief. (Lexico)
theism: Belief in the existence of a god or gods, specifically of a creator who intervenes in the universe. (ibid.)
Lexico points out that theism differs from deism:
deism: Belief in the existence of a supreme being, specifically of a creator who does not intervene in the universe. (ibid.)
[It's a pity that certain implementations — maybe all implementations — of Georgia don't contain all accented Greek characters. What appears as ὼ for example should look like ὼ
.]