The works of Yogarāja being very old clearly tells Anatta (not self) means not self of 'I' which is psycho-phyical. The term self in the 'not self' doesn't mean lack of super consciousness but lack of psycho-phyical consciousness. E.g, When we say - I'm doing, I'm eating, I'm playing etc. Here 'I' is psycho-phyical not real 'I'. Real 'I' is unchanging & permanent which is not supposed to do something, eat something, or play etc. This psycho-physical I is called as not-self because it is not our real self. That is what meant by Yogarāja, that I can say as I belong to the system you have mentioned Kashmiri Shaivism. So there is no conflict between Buddhists & Kashmiri Shaivism here. I've explained similar concept here. Also, read this one as well.
Following is an excerpt from Anatta-lakkhana Sutta: The Discourse on the Not-self Characteristic.
There he addressed the bhikkhus of the group of five: "Bhikkhus." — "Venerable sir," they replied. The Blessed One said this.
"Bhikkhus, form is not-self. Were form self, then this form would not
lead to affliction, and one could have it of form: 'Let my form be
thus, let my form be not thus.' And since form is not-self, so it
leads to affliction, and none can have it of form: 'Let my form be
thus, let my form be not thus.'
"Bhikkhus, feeling is not-self...
"Bhikkhus, perception is not-self...
"Bhikkhus, determinations are not-self...
"Bhikkhus, consciousness is not self. Were consciousness self, then
this consciousness would not lead to affliction, and one could have it
of consciousness: 'Let my consciousness be thus, let my consciousness
be not thus.' And since consciousness is not-self, so it leads to
affliction, and none can have it of consciousness: 'Let my
consciousness be thus, let my consciousness be not thus.'
"Bhikkhus, how do you conceive it: is form permanent or impermanent?" — "Impermanent, venerable Sir." — "Now is what is impermanent painful or pleasant?" — "Painful, venerable Sir." — "Now is what is impermanent, what is painful since subject to change, fit to be regarded thus: 'This is mine, this is I, this is my self'"? — "No, venerable sir."
"Is feeling permanent or impermanent?...
"Is perception permanent or impermanent?...
"Are determinations permanent or impermanent?...
"Is consciousness permanent or impermanent?" — "Impermanent, venerable
sir." — "Now is what is impermanent pleasant or painful?" — "Painful,
venerable sir." — "Now is what is impermanent, what is painful since
subject to change, fit to be regarded thus: 'This is mine, this is I,
this is my self'"? — "No, venerable sir."
"So, bhikkhus any kind of form whatever, whether past, future or
presently arisen, whether gross or subtle, whether in oneself or
external, whether inferior or superior, whether far or near, must with
right understanding how it is, be regarded thus: 'This is not mine,
this is not I, this is not myself.'
"Any kind of feeling whatever...
"Any kind of perception whatever...
"Any kind of determination whatever...
"Any kind of consciousness whatever, whether past, future or presently
arisen, whether gross or subtle, whether in oneself or external,
whether inferior or superior, whether far or near must, with right
understanding how it is, be regarded thus: 'This is not mine, this is
not I, this is not my self.'
"Bhikkhus, when a noble follower who has heard (the truth) sees thus,
he finds estrangement in form, he finds estrangement in feeling, he
finds estrangement in perception, he finds estrangement in
determinations, he finds estrangement in consciousness.
"When he finds estrangement, passion fades out. With the fading of
passion, he is liberated. When liberated, there is knowledge that he
is liberated. He understands: 'Birth is exhausted, the holy life has
been lived out, what can be done is done, of this there is no more
beyond.'"
That is what the Blessed One said. The bhikkhus were glad, and they approved his words.
Now during this utterance, the hearts of the bhikkhus of the group of five were liberated from taints through clinging no more.
Note - Consciousness meant by Gautam Buddha is psycho-phyical self explained above, not real self.