Factual errors:

• Interpreters neither need nor usually have a compilation step
• Even processors are nowadays virtual machines, modern hardware only understands microcode AFAIK

Words which have a common understanding in the current compiler construction world, which you define in IMHO a non standard way

• Compiler is commonly used to refer to tools which translate higher level languages (e.g. Java, C, Python, JavaScript) to a machine representation (e.g. JVM, Arm64, x86_64, MIPS...)
• Even in academia Java is referred to as compiled/interpreted language (at the same time)

Factual errors about Java:

• We have ahead of time compilers for a very long time now (GraalVM etc)
• There are chips which implement the JVM in hardware

all interpreters have a compilation step that produces machine code

Very much not a thing. JIT interpreters are actually not that common. Most interpreters parse code to an AST in memory and then run execute said AST, without any compilation to machine code.

the output of the standard javac compiler is not machine code that a processor understands. This is what makes Java not a compiled language.

Listen to yourself the output of the compiler makes it not a compiled language. Java is a compiled language, and jvm bytecode can be compiled (see graalvm), or interpreted (and when interpreted it can be JITd)

I think you're used to modern interpreted languages and are unaware of how the runtimes of interpreted languages used to work.

Something like Basic (to use a properly old example) was constantly interpreting source code during the entire run.

If I'm not mistaken Python was the first major interpreted language which by default interpreted the code into a binary format and then just ran the binary (and, if I remember it correctly, that wasn't the case in its first version). By this point Java already JIT compilation in its VM for a while.

I think you're committing the error of comparing modern interpreted languages with how Java worked 2 decades ago.